#### Answer

The augmented matrix is,
$\left[ \begin{matrix}
3 & -2 & 5 & 31 \\
1 & 3 & -3 & -12 \\
-2 & -5 & 3 & 11 \\
\end{matrix} \right]$

#### Work Step by Step

A system of linear equations can be solved with the help of matrices. One of the methods (gaussian elimination) to solve the system of the linear equations involves the augmented matrix.
When a matrix is separated into two groups by a vertical line, with the coefficients of the variable on one side and constants on the other side, it is called an augmented matrix. The coefficient of the missing variable is used as $0$ in the augmented matrix.
Hence, the augmented matrix for the provided system of equations is,
$\left[ \begin{matrix}
3 & -2 & 5 & 31 \\
1 & 3 & -3 & -12 \\
-2 & -5 & 3 & 11 \\
\end{matrix} \right]$