Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
4x & -3y & -z & =2\\
3x & -5y & +2z & =6\\
-3x & -6y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{2}&{-3}&{-4}\\
{3}&{-5}&{2}&{6}\\
{0}&{-11}&{6}&{12}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
4x & -3y & -z & =2\\
3x & -5y & +2z & =6\\
-3x & -6y & +4z & =6
\end{array}\right.$
Performing the row operations,
$R_{1}=-r_{2}+r_{1}$
$R_{3}=r_{2}+r_{3}$
$\left[\begin{array}{rrr|r}
{4}&{-3}&{-1}&{2}\\
{3}&{-5}&{2}&{6}\\
{-3}&{-6}&{4}&{6}\end{array}\right]\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{-(3)+4} &{-(-5)-3}&{-(2)-1}&{-(6)+2}\\
{3} &{-5} &{2} &{6}\\
{3+(-3)}&{-5+(-6)}&{2+4}&{6+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{2}&{-3}&{-4}\\
{3}&{-5}&{2}&{6}\\
{0}&{-11}&{6}&{12}\end{array}\right]$
