Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +2z & =-6\\
2x & -5y & +3z & =-4\\
-3x & -6y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{rrr|r}
{1}&{-3}&{2}&{-6}\\
{0}&{1}&{-1}&{8}\\
{0}&{-15}&{10}&{-12}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +2z & =-6\\
2x & -5y & +3z & =-4\\
-3x & -6y & +4z & =6
\end{array}\right.$
Performing the row operations,
$R_{2}=-2r_{1}+r_{2}$
$R_{3}=3r_{1}+r_{3}$
$\left[\begin{array}{rrr|r}
{1}&{-3}&{2}&{-6}\\
{2}&{-5}&{3}&{-4}\\
{-3}&{-6}&{4}&{6}\end{array}\right]\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{1} &{-3} &{2} &{-6}\\
{-2(1)+2} &{-2(-3)-5} &{-2(2)+3}&{-2(-6)-4}\\
{3(1)-3}&{3(-3)-6}&{3(2)+4}&{3(-6)+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{2}&{-6}\\
{0}&{1}&{-1}&{8}\\
{0}&{-15}&{10}&{-12}\end{array}\right]$
