Answer
$\begin{bmatrix}
-1&1 &1 & 3\\
0 & 3 & -2 &1 \\
-1 & 0 &2&0
\end{bmatrix}$.
Work Step by Step
The given system is
$\left\{\begin{matrix}
-x &+y &+z& = &3 \\
& 3y & -2z&= &1 \\
-x&&+2z&=&0
\end{matrix}\right.$
Rewrite the system by using missing variable with $0$ coefficient.
$\left\{\begin{matrix}
-x &+y &+z& = &3 \\
0x & +3y & -2z&= &1 \\
-x&+0y&+2z&=&0
\end{matrix}\right.$
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
$\begin{bmatrix}
-1&1 &1 & 3\\
0 & 3 & -2 &1 \\
-1 & 0 &2&0
\end{bmatrix}$.
