Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
5x & -3y & +z & =-2\\
2x & -5y & +6z & =-2\\
-4x & +y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{7}&{-11}&{2}\\
{2}&{-5}&{6}&{-2}\\
{0}&{-9}&{16}&{2}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
5x & -3y & +z & =-2\\
2x & -5y & +6z & =-2\\
-4x & +y & +4z & =6
\end{array}\right.$
Performing the row operations,
$R_{1}=-2r_{2}+r_{1}$
$R_{3}=2r_{2}+r_{3}$
$\left[\begin{array}{rrr|r}
{5}&{-3}&{1}&{-2}\\
{2}&{-5}&{6}&{-2}\\
{-4}&{1}&{4}&{6}\end{array}\right]\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{-2(2)+5} &{-2(-5)-3}&{-2(6)+1}&{-2(-2)-2}\\
{2} &{-5} &{6} &{-2}\\
{2(2)+(-4)}&{2(-5)+1}&{2(6)+4}&{2(-2)+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{7}&{-11}&{2}\\
{2}&{-5}&{6}&{-2}\\
{0}&{-9}&{16}&{2}\end{array}\right]$
