Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +3z & =-5\\
-4x & -5y & -3z & =-5\\
-3x & -2y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{3}&{-5}\\
{0}&{-17}&{9}&{-25}\\
{0}&{-11}&{13}&{-9}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & +3z & =-5\\
-4x & -5y & -3z & =-5\\
-3x & -2y & +4z & =6
\end{array}\right.$
Performing the row operations,
$R_{2}=4r_{1}+r_{2}$
$R_{3}=3r_{1}+r_{3}$
$\left[\begin{array}{rrr|r}
{1}&{-3}&{3}&{-5}\\
{-4}&{-5}&{-3}&{-5}\\
{-3}&{-2}&{4}&{6}\end{array}\right]\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{1} &{-3} &{3} &{-5}\\
{4(1)-4}&{4(-3)-5}&{4(3)-3}&{4(-5)-5}\\
{3(1)-3}&{3(-3)-2}&{3(3)+4}&{3(-5)+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{3}&{-5}\\
{0}&{-17}&{9}&{-25}\\
{0}&{-11}&{13}&{-9}\end{array}\right]$
