Answer
$\begin{bmatrix}
1&0 &3 & -1\\
-1 & -5 & 0 &6 \\
0 & 2 &-1&-3
\end{bmatrix}$.
Work Step by Step
The given system is
$\left\{\begin{matrix}
x & &+3z& = &-1 \\
-x & -5y & &= &6 \\
&2y&-z&=&-3
\end{matrix}\right.$
Rewrite the system by using missing variable with $0$ coefficient.
$\left\{\begin{matrix}
x & +0y &+3z& = &-1 \\
-x & -5y &+0z &= &6 \\
0x&2y&-z&=&-3
\end{matrix}\right.$
For the augmented matrix
First column $=$ coefficients of $x$.
Second column $=$ coefficients of $y$
third column $=$ coefficients of $z$
and fourth column $=$ the right-hand side.
The augmented matrix is
$\begin{bmatrix}
1&0 &3 & -1\\
-1 & -5 & 0 &6 \\
0 & 2 &-1&-3
\end{bmatrix}$.
