Answer
See the solution.
Work Step by Step
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.
Alternatively, you can say that there is a pivot in each column, meaning there are no free variables.
