Use the given of the coefficient matrix to solve the

vomiderawo 2021-11-19 Answered
Use the given of the coefficient matrix to solve the following system.
\(\displaystyle{7}{x}_{{1}}+{3}{x}_{{2}}={6}\)
\(\displaystyle-{6}{x}_{{1}}-{3}{x}_{{2}}={4}\)
\[A^{-1}=\begin{bmatrix}1&1\\-2&-\frac{7}{3}\end{bmatrix}\]

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Expert Answer

Michele Grimsley
Answered 2021-11-20 Author has 1367 answers

\(\displaystyle{7}{x}_{{1}}+{3}{x}_{{2}}={6}\)
\(\displaystyle-{6}{x}_{{1}}-{3}{x}_{{2}}={4}\)
Ax=B
\(\displaystyle\Rightarrow{x}={A}^{{-{1}}}{B}\)
Here \[A=\begin{bmatrix}7&3\\-6&-3\end{bmatrix}B=\begin{bmatrix}6\\4\end{bmatrix}\]
\[x=A^{-1}B=\begin{bmatrix}1&1\\-2&-\frac{7}{3}\end{bmatrix}\begin{bmatrix}6\\4\end{bmatrix}\]
\(\displaystyle{7}{x}_{{1}}+{3}{x}_{{2}}={6}\)
\(\displaystyle-{6}{x}_{{1}}-{3}{x}_{{2}}={4}\)
\(\displaystyle{A}{x}={B}\)
\(\displaystyle\Rightarrow{x}={A}^{{-{1}}}{B}\)
Here \[A=\begin{bmatrix}7&3\\-6&-3\end{bmatrix}B=\begin{bmatrix}6\\4\end{bmatrix}\]
\[=\begin{bmatrix}1&1\\-2&-\frac{7}{3}\end{bmatrix}\begin{bmatrix}6\\4\end{bmatrix}\]
\[=\begin{bmatrix}6+4\\-12-\frac{28}{3}\end{bmatrix}\]
\[=\begin{bmatrix}10\\-64/3\end{bmatrix}\]

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