Answer
The new matrix is,
$\left[ \begin{matrix}
1 & -3 & 2 & 5 \\
1 & 5 & -5 & 0 \\
3 & 0 & 4 & 7 \\
\end{matrix} \right]$
Work Step by Step
Consider the given matrix,
$\left[ \begin{matrix}
2 & -6 & 4 & 10 \\
1 & 5 & -5 & 0 \\
3 & 0 & 4 & 7 \\
\end{matrix} \right]$
The operation $\frac{1}{2}{{R}_{1}}$ implies that each element of row one will be multiplied by $\frac{1}{2}$.
The new matrix is obtained after performing row operation ${{R}_{1}}\to \frac{1}{2}{{R}_{1}}$. So,
$\left[ \begin{matrix}
\frac{1}{2}\times 2 & \frac{1}{2}\times (-6) & \frac{1}{2}\times 4 & \frac{1}{2}\times 10 \\
1 & 5 & -5 & 0 \\
3 & 0 & 4 & 7 \\
\end{matrix} \right]=\left[ \begin{matrix}
1 & -3 & 2 & 5 \\
1 & 5 & -5 & 0 \\
3 & 0 & 4 & 7 \\
\end{matrix} \right]$
Therefore, the new matrix is,
$\left[ \begin{matrix}
1 & -3 & 2 & 5 \\
1 & 5 & -5 & 0 \\
3 & 0 & 4 & 7 \\
\end{matrix} \right]$
