Answer
$\left\{ \left( 2,\ -3,\ 7 \right) \right\}$
Work Step by Step
The given system of equations can be written in matrix form as below: $\left[ \left. \begin{matrix}
2 & -1 & -1 \\
1 & 2 & 1 \\
3 & 4 & 2 \\
\end{matrix} \right|\begin{matrix}
0 \\
3 \\
8 \\
\end{matrix} \right]$
Now we will solve this matrix as below to get:
$\left[ \left. \begin{matrix}
2 & -1 & -1 \\
1 & 2 & 1 \\
0 & 2 & 1 \\
\end{matrix} \right|\begin{matrix}
0 \\
3 \\
1 \\
\end{matrix} \right]$ $ By,\ 3{{R}_{2}}-{{R}_{3}}\to {{R}_{3}}$
$\left[ \left. \begin{matrix}
2 & -1 & -1 \\
0 & 5 & 3 \\
0 & 2 & 1 \\
\end{matrix} \right|\begin{matrix}
0 \\
6 \\
1 \\
\end{matrix} \right]$ $ By,\ 2{{R}_{2}}-{{R}_{1}}\to {{R}_{2}}$
$\left[ \left. \begin{matrix}
2 & -1 & -1 \\
0 & 5 & 3 \\
0 & 1 & 0 \\
\end{matrix} \right|\begin{matrix}
0 \\
6 \\
-3 \\
\end{matrix} \right]$ $ By,\ 3{{R}_{3}}-{{R}_{2}}\to {{R}_{3}}$
Convert the matrix into equation form:
$\begin{align}
2x-y-z=0 & \\
5y+3z=6 & \\
y=-3 & \\
\end{align}$
Substitute the value of $ y $ in $5y+3z=6$ to obtain the value of $ z $:
$\begin{align}
& 5\times \left( -3 \right)+3z=6 \\
& 3z=6+15 \\
& 3z=21 \\
& z=7
\end{align}$
Substitute the value of $ y,z $ in $2x-y-z=0$ to obtain the value of $ x $:
$\begin{align}
& 2x-\left( -3 \right)-7=0 \\
& 2x=-3+7 \\
& 2x=4 \\
& x=2
\end{align}$
Hence, the solution is $\left\{ \left( 2,\ -3,\ 7 \right) \right\}$
