Answer
$ \left[\begin{array}{ccc|c}
1 & 2 & 2&2\\
0 & 1& -1& 2\\
0&0&9&-9
\end{array}\right]$.
Work Step by Step
The given matrix is
$\Rightarrow \left[\begin{array}{ccc|c}
1 & 2 & 2&2\\
0 & 1& -1& 2\\
0&5&4&1
\end{array}\right]$
Perform $R_3\rightarrow -5R_2+R_3$.
Multiply the second row by $-5$ and add to the third row.
$\Rightarrow \left[\begin{array}{ccc|c}
1 & 2 & 2&2\\
0 & 1& -1& 2\\
-5(0)+0&-5(1)+5&-5(-1)+4&-5(2)+1
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{ccc|c}
1 & 2 & 2&2\\
0 & 1& -1& 2\\
0&0&9&-9
\end{array}\right]$.
