Answer
The answer is $\left[\begin{array}{ccc|c}
1& -3 & 2&0 \\
0 &10 &-7& 7 \\
2&-2&1&3\\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{ccc|c}
1& -3 & 2&0 \\
3 &1 &-1&7 \\
2&-2&1&3\\
\end{array}\right]$
Perform $ -3R_1+R_2 $
Multiply row one by $-3$ and add to the row two as shown below.
$\left[\begin{array}{ccc|c}
1& -3 & 2&0 \\
-3\cdot 1+3 &-3\cdot (-3)+ 1 &-3\cdot 2-1&-3\cdot 0+ 7 \\
2&-2&1&3\\
\end{array}\right]$
Simplify.
$\left[\begin{array}{ccc|c}
1& -3 & 2&0 \\
-3+3 &9+ 1 &-6-1& 0+ 7 \\
2&-2&1&3\\
\end{array}\right]$
$\left[\begin{array}{ccc|c}
1& -3 & 2&0 \\
0 &10 &-7& 7 \\
2&-2&1&3\\
\end{array}\right]$.
