The matrix is not properly formatted.
However, I'm able to rearrange the question as:
[tex]\left[\begin{array}{ccc}1&1&1|-1\\-2&3&5|3\\3&2&4|1\end{array}\right][/tex]
Operations:
[tex]2R_1 + R_2 ->R_2[/tex]
[tex]-3R_1 +R_3 ->R_3[/tex]
Please note that the above may not reflect the original question. However, you should be able to implement my steps in your question.
Answer:
[tex]\left[\begin{array}{ccc}1&1&1|-1\\0&5&7|1\\0&-1&1|4\end{array}\right][/tex]
Step-by-step explanation:
The first operation:
[tex]2R_1 + R_2 ->R_2[/tex]
This means that the new second row (R2) is derived by:
Multiplying the first row (R1) by 2; add this to the second row
The row 1 elements are:
[tex]\left[\begin{array}{ccc}1&1&1|-1\end{array}\right][/tex]
Multiply by 2
[tex]2 * \left[\begin{array}{ccc}1&1&1|-1\end{array}\right] = \left[\begin{array}{ccc}2&2&2|-2\end{array}\right][/tex]
Add to row 2 elements are: [tex]\left[\begin{array}{ccc}-2&3&5|3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}2&2&2|-2\end{array}\right] + \left[\begin{array}{ccc}-2&3&5|3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&5&7|1\end{array}\right][/tex]
The second operation:
[tex]-3R_1 +R_3 ->R_3[/tex]
This means that the new third row (R3) is derived by:
Multiplying the first row (R1) by -3; add this to the third row
The row 1 elements are:
[tex]\left[\begin{array}{ccc}1&1&1|-1\end{array}\right][/tex]
Multiply by -3
[tex]-3 * \left[\begin{array}{ccc}1&1&1|-1\end{array}\right] = \left[\begin{array}{ccc}-3&-3&-3|3\end{array}\right][/tex]
Add to row 2 elements are: [tex]\left[\begin{array}{ccc}3&2&4|1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3&-3&-3|3\end{array}\right] + \left[\begin{array}{ccc}3&2&4|1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0&-1&1|4\end{array}\right][/tex]
Hence, the new matrix is:
[tex]\left[\begin{array}{ccc}1&1&1|-1\\0&5&7|1\\0&-1&1|4\end{array}\right][/tex]
