Sure! Let's go through the process to fill in the numbers resulting from the indicated row operation:
The original matrix is:
[tex]\[
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
3 & 4 & 5 & 5 \\
-1 & 2 & 1 & -1
\end{array}\right]
\][/tex]
We need to perform the row operation [tex]\(R_2 \leftrightarrow R_3\)[/tex]. This means we are swapping the second row with the third row.
Let's swap [tex]\(R_2\)[/tex] and [tex]\(R_3\)[/tex]:
- The first row remains the same: [tex]\([2, -1, -4, 7]\)[/tex]
- The second row after swapping will be the original third row: [tex]\([-1, 2, 1, -1]\)[/tex]
- The third row after swapping will be the original second row: [tex]\([3, 4, 5, 5]\)[/tex]
The resulting matrix after the row swap is:
[tex]\[
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
-1 & 2 & 1 & -1 \\
3 & 4 & 5 & 5
\end{array}\right]
\][/tex]
So, filling in the numbers, we get:
[tex]\[
\left[\begin{array}{ccc|c}
2 & -1 & -4 & 7 \\
-1 & 2 & 1 & -1 \\
3 & 4 & 5 & 5
\end{array}\right]
\][/tex]
