The following matrix is the augmented matrix
for the system \(Ax = b\).
\(\begin{bmatrix}
1 & -1 & 0 & 1 \\
1 & 0 & 1 & 2 \\
0 & 1 & 1 & 3
\end{bmatrix}\)
Then, the system has
no solution
a unique solution
infinitely many solutions
The answer is “no solution”.
Transforming the matrix into RREF gives
\(\begin{bmatrix}
1 & 0 & 1 & 0 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}.\)
The last row represents the equation \(0 = 1\) which does not have any
solution.