Answer
$\left[\begin{array}{rrr}
1 & -1 & 1\\
4 & -2 & -1\\
1 & 1 & 5\\
-1 & -1 & -1
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
2\\
2\\
2\\
2
\end{array}\right]$
Work Step by Step
Coefficient matrix: $A=\left[\begin{array}{lll}
1 & -1 & 1\\
4 & -2 & -1\\
1 & 1 & 5\\
-1 & -1 & -1
\end{array}\right]$
Constant matrix: $B=\left[\begin{array}{l}
2\\
2\\
2\\
2
\end{array}\right]$
Uknowns: $X=\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]$
$AX=B$
$\left[\begin{array}{lll}
1 & -1 & 1\\
4 & -2 & -1\\
1 & 1 & 5\\
-1 & -1 & -1
\end{array}\right]\left[\begin{array}{l}
x\\
y\\
z
\end{array}\right]=\left[\begin{array}{l}
2\\
2\\
2\\
2
\end{array}\right]$
