Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +4z & =3\\
3x & -5y & +6z & =6\\
-5x & +3y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{4}&{3}\\
{0}&{4}&{-6}&{-3}\\
{0}&{-12}&{24}&{21}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +4z & =3\\
3x & -5y & +6z & =6\\
-5x & +3y & +4z & =6
\end{array}\right.$
Performing the row operations,$\begin{array}{l}{R_{2}=-3 r_{1}+r_{2}} \\ {R_{3}=5 r_{1}+r_{3}}\end{array}$
$\left[\begin{array}{ccc|c}
{1}&{-3}&{4}&{3}\\
{3}&{-5}&{6}&{6}\\
{-5}&{3}&{4}&{6}\end{array}\right]\rightarrow\left[\begin{array}{ccc|c}
{1} &{-3} &{4} &{3}\\
{-3(1)+3}&{-3(-3)-5}&{-3(4)+6}&{-3(3)+6}\\
{5(1)-5}&{5(-3)+3}&{5(4)+4}&{5(3)+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{4}&{3}\\
{0}&{4}&{-6}&{-3}\\
{0}&{-12}&{24}&{21}\end{array}\right]$
