Question

Perform the indicated matrix row operation and write the new matrix

Answer 1

The given operation involves just swapping the two rows, so carrying out $R_1\leftrightarrow R_2$ on the matrix gives

$\left[\begin{array}{cc|c}5&5&5\\1&-\dfrac23&5\end{array}\right]\to\left[\begin{array}{cc|c}1&-\dfrac23&5\\5&5&5\end{array}\right]$