Answer
$\left[\begin{array}{cccc|c}
1 & -5 & 2&-2&4\\
0&1&-3&-1& 0 \\
0 & 15& -4& 5&-6\\
0&-19&12&-6&13
\end{array}\right]$.
Work Step by Step
The given augmented matrix is
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -5 & 2&-2&4\\
0&1&-3&-1& 0 \\
3 & 0& 2& -1&6\\
-4&1&4&2&-3
\end{array}\right]$
Perform $R_3\rightarrow -3R_1+R_3$ and $R_4\rightarrow 4R_1+R_4$.
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -5 & 2&-2&4\\
0&1&-3&-1& 0 \\
-3(1)+3 & -3(-5)+0& -3(2)+2& -3(-2)-1&-3(4)+6\\
4(1)-4&4(-5)+1&4(2)+4&4(-2)+2&4(4)-3
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cccc|c}
1 & -5 & 2&-2&4\\
0&1&-3&-1& 0 \\
0 & 15& -4& 5&-6\\
0&-19&12&-6&13
\end{array}\right]$.
