Answer
The new matrix is,
$\left[ \begin{matrix}
1 & -1 & 5 & -6 \\
0 & 6 & -16 & -8 \\
1 & 3 & 2 & 5 \\
\end{matrix} \right]$
Work Step by Step
Consider the provided matrix,
$\left[ \begin{matrix}
1 & -1 & 5 & -6 \\
3 & 3 & -1 & 10 \\
1 & 3 & 2 & 5 \\
\end{matrix} \right]$
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 second row.
The new matrix is obtained after performing the row operation ${{R}_{2}}\to -3{{R}_{1}}+{{R}_{2}}$
$\left[ \begin{matrix}
1 & -1 & 5 & -6 \\
-3+3 & 3+3 & -15-1 & -18+10 \\
1 & 3 & 2 & 5 \\
\end{matrix} \right]=\left[ \begin{matrix}
1 & -1 & 5 & -6 \\
0 & 6 & -16 & -8 \\
1 & 3 & 2 & 5 \\
\end{matrix} \right]$
Therefore, the new matrix is
$\left[ \begin{matrix}
1 & -1 & 5 & -6 \\
0 & 6 & -16 & -8 \\
1 & 3 & 2 & 5 \\
\end{matrix} \right]$
