Answer
The answer is $\left[\begin{array}{ccc|c}
1& 2 & 1&2 \\
0&3 &4&9 \\
0&1&-3&- 10\\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{ccc|c}
1& 2 & 1&2 \\
-2 &-1 &2&5 \\
1&3&-2&-8\\
\end{array}\right]$
Perform $ 2R_1+R_2 $ and $ -1R_1+R_3 $.
Multiply row one by $2$ and add to row two.
Multiply row one by $ -1$ and add to row three.
$\left[\begin{array}{ccc|c}
1& 2 & 1&2 \\
2\cdot 1-2 &2\cdot 2-1 &2\cdot 1+2&2\cdot 2+5 \\
-1\cdot 1+1&-1\cdot 2+3&-1\cdot 1-2&-1\cdot 2-8\\
\end{array}\right]$
Simplify.
$\left[\begin{array}{ccc|c}
1& 2 & 1&2 \\
2-2 &4-1 &2+2&4+5 \\
-1+1&- 2+3&-1-2&- 2-8\\
\end{array}\right]$
$\left[\begin{array}{ccc|c}
1& 2 & 1&2 \\
0&3 &4&9 \\
0&1&-3&- 10\\
\end{array}\right]$.
