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

I don't understand how to do this at all, and I need to have the work shown. (Matrices-example-1
User Sanchit
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1 Answer

2 votes

Answer:

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]

User Suran
by
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