## Linear Algebra and Its Applications (5th Edition)

The reduced row echelon form of the augmented matrix is $\left[ \begin{array}{cccc} 1 & 0 & 0 &a_1\\ 0 & 1&0&a_2\\ 0&0&1&a_3 \end{array} \right],$ where $a_1$, $a_2$, and $a_3$ are numbers. We can see the last column (on the right) is not a pivot column and the corresponding system of equations will have no free variables. Hence the system is consistent and has a unique solution.