Answer
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -1 & 1&1& 3\\
0&1&-2&-1& 0 \\
0 & 2& 1& 2&5\\
0&6&-3&-1&-9
\end{array}\right]$.
Work Step by Step
The given augmented matrix is
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -1 & 1&1& 3\\
0&1&-2&-1& 0 \\
2 & 0& 3& 4&11\\
5&1&2&4&6
\end{array}\right]$
Perform $R_3\rightarrow -2R_1+R_3$ and $R_4\rightarrow -5R_1+R_4$.
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -1 & 1&1& 3\\
0&1&-2&-1& 0 \\
-2(1)+2 & -2(-1)+0& -2(1)+3& -2(1)+4&-2(3)+11\\
-5(1)+5&-5(-1)+1&-5(1)+2&-5(1)+4&-5(3)+6
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -1 & 1&1& 3\\
0&1&-2&-1& 0 \\
0 & 2& 1& 2&5\\
0&6&-3&-1&-9
\end{array}\right]$.
