Perform the following matrix row operation and write the new matrix.
\[
\left[\begin{array}{rrr|r}
3 & -9 & 15 & 18 \\
-3 & 7 & 6 & 0 \\
-7 & 0 & 5 & 3
\end{array}\right] \frac{1}{3} R_{1}
\]

Step 1 ：Given the matrix \[\left[\begin{array}{rrr|r} 3 & -9 & 15 & 18 \\ -3 & 7 & 6 & 0 \\ -7 & 0 & 5 & 3 \end{array}\right]\]

Step 2 ：We are asked to perform the row operation \(\frac{1}{3} R_{1}\) on the given matrix. This operation will not affect the other rows.

Step 3 ：Performing the operation, we get the new first row as \([ 1, -3, 5, 6 ]\)

Step 4 ：Substituting this new row into the original matrix, we get the new matrix as \[\left[\begin{array}{rrr|r} 1 & -3 & 5 & 6 \\ -3 & 7 & 6 & 0 \\ -7 & 0 & 5 & 3 \end{array}\right]\]

Step 5 ：\(\boxed{\left[\begin{array}{rrr|r} 1 & -3 & 5 & 6 \\ -3 & 7 & 6 & 0 \\ -7 & 0 & 5 & 3 \end{array}\right]}\) is the final answer after performing the row operation.