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

The reduced row echelon form of the augmented matrix is $\left[ \begin{array}{cccc} 1 & 0 & 0 &...&0&a_1\\ 0 & 1&0&...&0&a_2\\ \vdots & &\ddots & &0&\vdots \\ \vdots & & &\ddots \\ 0& ...&...&...&1&a_n \end{array} \right],$ where $a_1$,...,$a_n$ 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.