Correct
Fill in the blank by performing the indicated elementary row operation(s).
\[
\left[\begin{array}{ccc|c}
-3 & -6 & 15 & 15 \\
1 & 2 & -5 & -5 \\
-8 & 2 & -9 & 7
\end{array}\right] \stackrel{3 R_{2}+R_{1},-15 R_{2}+R_{3}}{\longrightarrow} ?
\]
Answer
The matrix after performing the elementary row operations is \[\left[\begin{array}{ccc|c} 0 & 0 & 0 & 0 \\ 1 & 2 & -5 & -5 \\ -23 & -28 & 66 & 82 \end{array}\right]\]
Step 1 ：Multiply the second row by 3 to get \([3, 6, -15, -15]\)
Step 2 ：Add the result to the first row to get \([0, 0, 0, 0]\)
Step 3 ：Multiply the second row by -15 to get \([-15, -30, 75, 75]\)
Step 4 ：Add the result to the third row to get \([-23, -28, 66, 82]\)
Step 5 ：The matrix after performing the elementary row operations is \[\left[\begin{array}{ccc|c} 0 & 0 & 0 & 0 \\ 1 & 2 & -5 & -5 \\ -23 & -28 & 66 & 82 \end{array}\right]\]
