Answer
The new matrix is,
$\left[ \begin{matrix}
1 & -3 & 2 & 0 \\
0 & 10 & -7 & 7 \\
2 & -2 & 1 & 3 \\
\end{matrix} \right]$
Work Step by Step
Consider the provided matrix,
$\left[ \begin{matrix}
1 & -3 & 2 & 0 \\
3 & 1 & -1 & 7 \\
2 & -2 & 1 & 3 \\
\end{matrix} \right]$
The operation $-3{{R}_{1}}+{{R}_{2}}$ implies that each element of the first row will be multiplied by $-3$ and then added with the corresponding element of the row second.
The new matrix is obtained after performing the row operation ${{R}_{2}}\to -3{{R}_{1}}+{{R}_{2}}$ ,
$\left[ \begin{matrix}
1 & -3 & 2 & 0 \\
-3+3 & 9+1 & -6-1 & 0+7 \\
2 & -2 & 1 & 3 \\
\end{matrix} \right]=\left[ \begin{matrix}
1 & -3 & 2 & 0 \\
0 & 10 & -7 & 7 \\
2 & -2 & 1 & 3 \\
\end{matrix} \right]$
Therefore, the new matrix is,
$\left[ \begin{matrix}
1 & -3 & 2 & 0 \\
0 & 10 & -7 & 7 \\
2 & -2 & 1 & 3 \\
\end{matrix} \right]$
