To transform the matrix [tex]\(\left[\begin{array}{ccc}5 & 1 & 2 \\ 2 & -2 & 6 \\ 7 & 0 & 1 \end{array}\right]\)[/tex] into the matrix [tex]\(\left[\begin{array}{ccc}1 & -1 & 3 \\ 0 & 6 & -13 \\ 7 & 0 & 1 \end{array}\right]\)[/tex], we can follow these row operations:
1. Multiply [tex]\( R_2 \)[/tex] by [tex]\(\frac{1}{2}\)[/tex] to get [1, -1, 3] in the second row.
2. Replace [tex]\( R_1 \)[/tex] with [tex]\(-5 R_2 + R_1\)[/tex].
3. No further row operations are necessary to achieve the desired matrix format.
This sequence of operations can be represented as:
- [tex]\(\frac{1}{2} R_2\)[/tex]
- [tex]\(-5 R_2 + R_1\)[/tex] replaces [tex]\(R_1\)[/tex]
The correct choices to fill the boxes would be:
[tex]\[
\begin{array}{|c|}
\hline
\frac{1}{2} R_2 \\
\hline
-5 R_2 + R_1\; replaces R_1 \\
\hline
\square\\
\hline
\end{array}
\][/tex]
Note:
The operation 'switch [tex]\(R_2\)[/tex] and [tex]\(R_1\)[/tex]' is not part of the sequence and thus not needed.
