Answer
The answer is $\left[\begin{array}{ccc|c}
1& 1 & -1&6 \\
0 &-3 &3&-15 \\
0&-4&2&-14\\
\end{array}\right]$.
Work Step by Step
The given matrix is
$\left[\begin{array}{ccc|c}
1& 1 & -1&6 \\
2 &-1 &1&-3 \\
3&-1&-1&4\\
\end{array}\right]$
Perform $ -2R_1+R_2 $ and $ -3R_1+R_3 $
Multiply row one by $-2 $ and add to row two.
Multiply row one by $ -3 $ and add to row three.
$\left[\begin{array}{ccc|c}
1& 1 & -1&6 \\
-2 \cdot 1+2 &-2 \cdot 1-1 &-2 \cdot (-1)+1&-2 \cdot (6)-3 \\
-3\cdot 1+3&-3\cdot 1-1&-3\cdot (-1)-1&-3\cdot (6)+4\\
\end{array}\right]$
Simplify.
$\left[\begin{array}{ccc|c}
1& 1 & -1&6 \\
-2 +2 &-2 -1 &2+1&-12-3 \\
-3+3&-3-1&3-1&-18+4\\
\end{array}\right]$
$\left[\begin{array}{ccc|c}
1& 1 & -1&6 \\
0 &-3 &3&-15 \\
0&-4&2&-14\\
\end{array}\right]$.
