Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & -4z & =-6\\
26x & -5y & +6z & =-6\\
-x & +y & +4z & =6
\end{array}\right.$
Performing the row operations,
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{-4}&{-6}\\
{6}&{-5}&{6}&{-6}\\
{0}&{-2}&{0}&{0}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{llll}
x & -3y & -4z & =-6\\
26x & -5y & +6z & =-6\\
-x & +y & +4z & =6
\end{array}\right.$
Performing the row operations,
$R_{2}=-6r_{1}+r_{2}$
$R_{3}=r_{1}+r_{3}$
$\left[\begin{array}{ccc|c}
{1}&{-3}&{-4}&{-6}\\
{6}&{-5}&{6}&{-6}\\
{-1}&{1}&{4}&{6}\end{array}\right]\rightarrow$
$\rightarrow\left[\begin{array}{ccc|c}
{1} &{-3} &{-4} &{-6}\\
{-6(1)+6}&{-6(-3)-5}&{-6(-4)+6}&{-6(-6)-6}\\
{1-1} &{-3+1} &{-4+4} &{-6+6}\end{array}\right]$
$\rightarrow\left[\begin{array}{ccc|c}
{1}&{-3}&{-4}&{-6}\\
{6}&{-5}&{6}&{-6}\\
{0}&{-2}&{0}&{0}\end{array}\right]$
