Answer
The answer is $\left[\begin{array}{ccc|c}
1& -1 & 5&-6 \\
0 &6 &-16&28 \\
1&3&2&5\\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{ccc|c}
1& -1 & 5&-6 \\
3 &3 &-1& 10 \\
1&3&2&5\\
\end{array}\right]$
Perform $ -3R_1+R_2 $.
Multiply row one by $ -3$ and add to the row two as shown below.
$\left[\begin{array}{ccc|c}
1& -1 & 5&-6 \\
-3\cdot 1 +3 &-3\cdot (-1)+3 &-3\cdot(5)-1&-3\cdot (-6)+ 10 \\
1&3&2&5\\
\end{array}\right]$
Simplify.
$\left[\begin{array}{ccc|c}
1& -1 & 5&-6 \\
-3 +3 &3+3 &-15-1&18+ 10 \\
1&3&2&5\\
\end{array}\right]$
$\left[\begin{array}{ccc|c}
1& -1 & 5&-6 \\
0 &6 &-16&28 \\
1&3&2&5\\
\end{array}\right]$.
