Use the indicated row operation to transform \( \left[\begin{array}{ccc|c}5 & -25 & 10 & 20 \\ -8 & 0 & -7 & 1 \\ 6 & 7 & 8 & 0\end{array}\right] \). Replace \( R_{1} \) by \( \frac{1}{5} R_{1} \). The transformed matrix is \( \square \)

To transform the given matrix by replacing \( R_{1} \) with \( \frac{1}{5} R_{1} \), we will divide each element in the first row by 5. Starting with the first row \( [5, -25, 10, 20] \), we perform the operations: - \( \frac{1}{5} \times 5 = 1 \) - \( \frac{1}{5} \times -25 = -5 \) - \( \frac{1}{5} \times 10 = 2 \) - \( \frac{1}{5} \times 20 = 4 \) Therefore, the transformed row \( R_{1} \) becomes \( [1, -5, 2, 4] \). The transformed matrix will be: \[ \left[\begin{array}{ccc|c}1 & -5 & 2 & 4 \\ -8 & 0 & -7 & 1 \\ 6 & 7 & 8 & 0\end{array}\right] \]