Perform the row operation on the given augmented matrix.
\[
\left[\begin{array}{rrr|r}
1 & 5 & -7 & -9 \\
2 & 4 & 5 & 6 \\
-5 & 1 & 4 & 1
\end{array}\right] \quad-2 R_{1}+R_{2}
\]
What is the resultant matrix?
\[
\left[\begin{array}{l}
\square \square \square \mid \square \\
\square \square \square[ \\
\square \square \square \mid \square
\end{array}\right]
\]
Answer
So, the resultant matrix is: \[\left[\begin{array}{rrr|r} 1 & 5 & -7 & -9 \\ 0 & -6 & 19 & 24 \\ -5 & 1 & 4 & 1 \end{array}\right]\]
Step 1 ：Given operation is -2R1 + R2, which means we need to multiply the first row by -2 and then add it to the second row. The result will replace the second row. The first and third rows remain unchanged.
Step 2 ：Perform the operation: -2R1 + R2 = -2*(1, 5, -7, -9) + (2, 4, 5, 6) = (-2, -10, 14, 18) + (2, 4, 5, 6) = (0, -6, 19, 24)
Step 3 ：So, the resultant matrix is: \[\left[\begin{array}{rrr|r} 1 & 5 & -7 & -9 \\ 0 & -6 & 19 & 24 \\ -5 & 1 & 4 & 1 \end{array}\right]\]
