Answer
The columns in the coefficient matrix are all pivot columns.
Work Step by Step
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.
