Question

[1, 3, -1 | 2; 2, 5, 2 | 3; -3, -4, 6 | 0] perform the row operations and write resulting matrix. -2R1 +R2 -> R2 & 3R1+R3 -> R3

Answer 1

`\left[\begin{array}{ccc}1&3&-1\\0&-1&4\\0&5&3\end{array}\right]`:
`\left[\begin{array}{ccc}2\\0\\6\end{array}\right]`

Explanation:

We are given a matrix

Let A=
`\left[\begin{array}{ccc}1&3&-1\\2&5&2\\-3&-4&6\end{array}\right]`

and B=
`\left[\begin{array}{ccc}2\\2\\0\end{array}\right]`

We have to find the resulting matrix after performing given row operations

Apply
`R_2\rightarrow R_2-2R_1`

`\left[\begin{array}{ccc}1&3&-1\\0&-1&4\\-3&-4&6\end{array}\right]`:
`\left[\begin{array}{ccc}2\\0\\0\end{array}\right]`

Again apply
`R_3\rightarrow R_3+3R_1`

`\left[\begin{array}{ccc}1&3&-1\\0&-1&4\\0&5&3\end{array}\right]`:
`\left[\begin{array}{ccc}2\\0\\6\end{array}\right]`

Hence, resulting matrix

`\left[\begin{array}{ccc}1&3&-1\\0&-1&4\\0&5&3\end{array}\right]`:
`\left[\begin{array}{ccc}2\\0\\6\end{array}\right]`