Connect with experts and get insightful answers to your questions on IDNLearn.com. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
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]