Question

Given $M\times \left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}1& 2\end{array}\right]$
Find:
(i)The order of matrix $M$ ?
(ii)The matrix $M$. ?

Answer 1

$\left(1\right)M_{a,b}\times {\left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]}_{2\times 2}={\left[12\right]}_{1\times 2}$

$(a,b)=(1,2)$

$\left(2\right)\left[cd\right]\left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]=\left[12\right]$

$[cc+29]=\left[12\right]$

$c=1c+2d=2\Rightarrow 2d=1\Rightarrow d=1/2$

$M=\left[11/2\right]$