Title: Consistency

Q: Created by: Dr. Pang Chung Yin Amy, Dr. Chiang Shun Ling, and Naw Sai.
Department of Mathematics,
Hong Kong Baptist University (HKBU) © 2025.
A: These decks may be freely shared and distributed among students and educators. We hope they help in your linear algebra journey!

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 3 \\ 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 1 \\ 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 1 \\ 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 3 \\ 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 0 \\ 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 3 \\ 0 & 1 & 2 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 1 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 3 & 2 \\ 0 & 1 & 3 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 3 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 0 \\ 0 & 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 2 \\ 0 & 1 & 2 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 3 \\ 0 & 1 & 0 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 0 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 2 \\ 0 & 1 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 2 & 0 \\ 0 & 1 & 2 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 3 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 2 & 3 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 0 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 3 & 3 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 2 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 2 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 3 & 2 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 3 & 0 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 1 & 1 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 3 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 3 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 2 & 1 \\ 0 & 1 & 3 & 0 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 2 & 0 \\ 0 & 0 & 1 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 2 & 1 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 3 & 0 & 3 \\ 0 & 0 & 1 & 3 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 2 & 2 \\ 0 & 1 & 1 & 3 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 0 & 3 \\ 0 & 0 & 1 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 2 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 1 & 2 & 1 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 1 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 2 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 0 & 1 & 2 \\ 0 & 1 & 0 & 0 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 2 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 1 & 3 \\ 0 & 0 & 1 & 2 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 2 & 2 \\ 0 & 1 & 0 & 3 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 3 & 2 & 0 \\ 0 & 1 & 2 & 0 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 1 & 2 \\ 0 & 1 & 1 & 2 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 0 & 0 & 3 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 2 & 2 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 1 & 1 \\ 0 & 1 & 3 & 3 & 3 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 2 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 2 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 1 & 2 & 1 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 0 & 2 & 3 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 2 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 1 & 2 \\ 0 & 1 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 0 & 2 \\ 0 & 1 & 3 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 3 & 3 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 0 & 1 \\ 0 & 1 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 3 & 1 \\ 0 & 1 & 2 & 0 & 2 \\ 0 & 0 & 0 & 1 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 2 & 1 \\ 0 & 1 & 2 & 3 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right]$
A: Yes, the system is consistent.
The augmented matrix is in echelon form, and since there is no row of the form [0 ... 0 | nonzero], the system is consistent.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 0 \\ 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 2 \\ 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 1 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 3 \\ 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 1 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 1 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 3 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 1 & 0 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 2 \\ 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 1 & 3 \\ 0 & 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 3 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 0 & 3 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 2 \\ 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 0 & 4 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 3 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 0 \\ 0 & 0 & 5 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 0 & 3 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 2 \\ 0 & 1 & 1 \\ 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 1 & 2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 3 & 2 \\ 0 & 1 & 3 & 3 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 2 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 3 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 1 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 3 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 1 & 0 \\ 0 & 1 & 2 & 2 \\ 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 0 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 1 & 3 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 2 & 3 \\ 0 & 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 5 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 & 1 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 0 & 0 & 3 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 1 & 1 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 4 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 0 & 2 \\ 0 & 1 & 1 & 3 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 1 & 1 \\ 0 & 1 & 3 & 1 & 2 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 3 & 0 \\ 0 & 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 3 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 0 & 0 \\ 0 & 1 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: Determine if the following system is consistent. The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 1 & 2 \\ 0 & 1 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system is inconsistent. The augmented matrix is in echelon form and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 3 \\ 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 1 \\ 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 1 \\ 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 3 \\ 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 0 \\ 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 3 \\ 0 & 1 & 2 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 1 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 3 & 2 \\ 0 & 1 & 3 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 3 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 0 \\ 0 & 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 0 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 2 \\ 0 & 1 & 2 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 2 \\ 0 & 1 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 3 \\ 0 & 1 & 0 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 0 \\ 0 & 1 & 2 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 2 \\ 0 & 1 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 2 & 0 \\ 0 & 1 & 2 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 3 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 2 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 2 & 3 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 0 \\ 0 & 1 & 1 & 3 \\ 0 & 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 3 & 3 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 2 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 2 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 0 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 0 & 1 \\ 0 & 1 & 3 & 2 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 3 & 0 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 1 & 1 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 1 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 2 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 1 & 3 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There is exactly one solution because there are no free variables.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 3 & 3 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 2 & 1 \\ 0 & 1 & 3 & 0 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 2 & 0 \\ 0 & 0 & 1 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 2 & 1 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 3 & 0 & 3 \\ 0 & 0 & 1 & 3 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 2 & 2 \\ 0 & 1 & 1 & 3 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 0 & 3 \\ 0 & 0 & 1 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 2 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 1 & 2 & 1 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 1 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 2 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 0 & 1 & 2 \\ 0 & 1 & 0 & 0 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 2 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 1 & 3 \\ 0 & 0 & 1 & 2 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 2 & 2 \\ 0 & 1 & 0 & 3 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 3 & 2 & 0 \\ 0 & 1 & 2 & 0 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 1 & 2 \\ 0 & 1 & 1 & 2 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(3, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 0 & 0 & 3 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 0 & 2 & 2 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 1 & 1 \\ 0 & 1 & 3 & 3 & 3 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 2 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 2 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 1 & 2 & 1 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 0 & 2 & 3 \\ 0 & 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 2 & 1 & 0 \\ 0 & 0 & 1 & 1 & 1 \\ 0 & 0 & 0 & 1 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 3 & 1 & 2 \\ 0 & 1 & 1 & 3 & 3 \\ 0 & 0 & 1 & 2 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 0 & 2 \\ 0 & 1 & 3 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 3 & 1 & 0 & 2 \\ 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there are free variables in columns(2, 4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 3 & 3 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 2 & 3 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 0 & 1 \\ 0 & 1 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 2 & 3 & 1 \\ 0 & 1 & 2 & 0 & 2 \\ 0 & 0 & 0 & 1 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(3).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 2 & 1 \\ 0 & 1 & 2 & 3 & 0 \\ 0 & 0 & 1 & 0 & 1 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(4).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 1 & 1 & 1 & 0 \\ 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right]$
A: The system is consistent.
This is because the augmented matrix is in echelon form, and there is no row of the form [0 ... 0 | nonzero].
There are infinitely many solutions because there is a free variable in column(2).

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 0 & 2 \\ 0 & 1 & 1 & 3 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 1 \\ 0 & 1 & 3 \\ 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 0 \\ 0 & 0 & 5 \\ 0 & 0 & 0 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 4 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 3 & 1 & 1 \\ 0 & 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 4 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 2 & 3 & 0 \\ 0 & 0 & 1 & 3 & 2 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 3 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 2 \\ 0 & 1 & 2 & 0 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 0 & 2 \\ 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 1 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 1 & 0 \\ 0 & 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 0 & 1 & 2 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 1 & 2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 0 & 1 & 1 \\ 0 & 1 & 3 & 1 & 2 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 1 & 2 \\ 0 & 1 & 2 \\ 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 5 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 5], which represents the equation 0 = 5. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 0 & 0 \\ 0 & 1 & 1 & 2 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 1 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 2 & 1 & 3 \\ 0 & 0 & 0 & 4 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 4], which represents the equation 0 = 4. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 3 & 2 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 1], which represents the equation 0 = 1. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cccc|c} 1 & 2 & 3 & 0 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 0 & 2 & 2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 3 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 3 is of the form [0 ... 0 | 3], which represents the equation 0 = 3. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{cc|c} 1 & 0 & 3 \\ 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.

Q: How many solutions does the following system have? The augmented matrix in echelon form is $\left[\begin{array}{ccc|c} 1 & 3 & 3 & 3 \\ 0 & 0 & 0 & 2 \end{array}\right]$
A: The system has no solutions.
The system is inconsistent.
This is because the augmented matrix is in echelon form, and row 2 is of the form [0 ... 0 | 2], which represents the equation 0 = 2. This is a contradiction.