Question

I don't understand how to do this at all, and I need to have the work shown. (Matrices)

Answer 1

See below

Explanation:

`\left[\begin{array}{ccc}2&-8&22\\1&7&0\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&-4&11\\1&7&0\end{array}\right]`

Above we have
`(1)/(2)\cdot R_1 \rightarrow R_1`

Here we multiplied the first row by
`(1)/(2)`

Then,
`R_2-1\cdot R_1 \rightarrow R_2`

`\left[\begin{array}{ccc}1&-4&11\\1&7&11\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&-4&11\\0&11&-11\end{array}\right]`

Later,
`(1)/(11)\cdot R_2 \rightarrow R_2`

`\left[\begin{array}{ccc}1&-4&11\\0&11&-11\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&-4&11\\0&1&-1\end{array}\right]`

Finally,
`R_1+4\cdot R_2 \rightarrow R_1`

`\left[\begin{array}{ccc}1&-4&11\\0&1&-1\end{array}\right]\longrightarrow \left[\begin{array}{ccc}1&0&7\\0&1&-1\end{array}\right]`

Therefore, the complete process is

`\left[\begin{array}{ccc}2&-8&22\\1&7&0\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&-4&11\\1&7&0\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&-4&11\\0&11&-11\end{array}\right]`

`\longrightarrow \left[\begin{array}{ccc}1&-4&11\\0&1&-1\end{array}\right] \longrightarrow \left[\begin{array}{ccc}1&0&7\\0&1&-1\end{array}\right]`