Question

How to solve number 21 :/

Answer 1

`\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\frac{ \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)`


`\left(\begin{array}{cc}1&1\\-2&1\end{array}\right)^(-1)=(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)=(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}(1)/(3)&-(1)/(3)\\(2)/(3)&(1)/(3)\end{array}\right)\\\\`

`\bold{M}= 2\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\left(\begin{array}{cc}(1)/(3)&-(1)/(3)\\(2)/(3)&(1)/(3)\end{array}\right)\\ \bold{M}= 2\left(\begin{array}{cc}(1)/(3)&-(1)/(3)\\(2)/(3)&(1)/(3)\end{array}\right)\\ \bold{M}= \left(\begin{array}{cc}(2)/(3)&-(2)/(3)\\(4)/(3)&(2)/(3)\end{array}\right)`