Answer
The linear system can be written as:
$\begin{align}
& -x+z=-4 \\
& -y=2 \\
& y+z=4
\end{align}$
Work Step by Step
Now, compare the coefficients with the provided matrix
$\begin{align}
& {{a}_{1}}=-1 \\
& {{a}_{2}}=0 \\
& {{a}_{3}}=0
\end{align}$
$\begin{align}
& {{b}_{1}}=0 \\
& {{b}_{2}}=-1 \\
& {{b}_{3}}=1
\end{align}$
$\begin{align}
& {{c}_{1}}=1 \\
& {{c}_{2}}=0 \\
& {{c}_{3}}=1
\end{align}$ And $\begin{align}
& {{d}_{1}}=-4 \\
& {{d}_{2}}=2 \\
& {{d}_{3}}=4
\end{align}$
Substitute the values in the linear equation
$\begin{align}
& {{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}} \\
& {{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}} \\
& {{a}_{3}}x+{{b}_{2}}y+{{c}_{3}}z={{d}_{3}}
\end{align}$
So, $\begin{align}
& -x+z=-4 \\
& -y=2 \\
& y+z=4
\end{align}$
