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How to solve number 21 :/

How To Solve Number 21 class=

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konrad509
[tex] \left(\begin{array}{cc}1&1\\-2&1\end{array}\right) \bold{M}= 2\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\\ \bold{M}=2\dfrac{ \left(\begin{array}{cc}1&0\\0&1\end{array}\right) }{ \left(\begin{array}{cc}1&1\\-2&1\end{array}\right)}\\ \bold{M}=2\left(\begin{array}{cc}1&0\\0&1\end{array}\right) \left(\begin{array}{cc}1&1\\-2&1\end{array}\right)^{-1} [/tex]

[tex]\left(\begin{array}{cc}1&1\\-2&1\end{array}\right)^{-1}=\dfrac{1}{1-(-2)}\left(\begin{array}{cc}1&-1\\2&1\end{array}\right)\\ \left(\begin{array}{cc}1&1\\-2&1\end{array}\right)^{-1}=\dfrac{1}{3}\left(\begin{array}{cc}1&-1\\2&1\end{array}\right)\\ \left(\begin{array}{cc}1&1\\-2&1\end{array}\right)^{-1}=\left(\begin{array}{cc}\dfrac{1}{3}&-\dfrac{1}{3}\\\dfrac{2}{3}&\dfrac{1}{3}\end{array}\right)\\\\[/tex]
[tex] \bold{M}= 2\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\left(\begin{array}{cc}\dfrac{1}{3}&-\dfrac{1}{3}\\\dfrac{2}{3}&\dfrac{1}{3}\end{array}\right)\\ \bold{M}= 2\left(\begin{array}{cc}\dfrac{1}{3}&-\dfrac{1}{3}\\\dfrac{2}{3}&\dfrac{1}{3}\end{array}\right)\\ \bold{M}= \left(\begin{array}{cc}\dfrac{2}{3}&-\dfrac{2}{3}\\\dfrac{4}{3}&\dfrac{2}{3}\end{array}\right)[/tex]
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