Answer
The new matrix is,
$\left[ \begin{matrix}
1 & -4 & 2 & 3 \\
1 & -4 & 4 & 0 \\
2 & 0 & 7 & 4 \\
\end{matrix} \right]$
Work Step by Step
Consider the given matrix,
$\left[ \begin{matrix}
3 & -12 & 6 & 9 \\
1 & -4 & 4 & 0 \\
2 & 0 & 7 & 4 \\
\end{matrix} \right]$
The operation $\frac{1}{3}{{R}_{1}}$ implies that each element of row one will be multiplied by $\frac{1}{3}$.
The new matrix is obtained after performing the row operation ${{R}_{1}}\to \frac{1}{3}{{R}_{1}}$.
$\left[ \begin{matrix}
\frac{1}{3}\times 3 & \frac{1}{3}\times (-12) & \frac{1}{3}\times 6 & \frac{1}{3}\times 9 \\
1 & -4 & 4 & 0 \\
2 & 0 & 7 & 4 \\
\end{matrix} \right]=\left[ \begin{matrix}
1 & -4 & 2 & 3 \\
1 & -4 & 4 & 0 \\
2 & 0 & 7 & 4 \\
\end{matrix} \right]$
Therefore, the new matrix is,
$\left[ \begin{matrix}
1 & -4 & 2 & 3 \\
1 & -4 & 4 & 0 \\
2 & 0 & 7 & 4 \\
\end{matrix} \right]$
