Find x and y, if $2\left[ {\begin{array}{cccccccccccccccccccc}1&3\\0&x\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}y&0\\1&2\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}5&6\\1&8\end{array}} \right]$

.:

We have, $2\left[ {\begin{array}{cccccccccccccccccccc}1&3\\0&x\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}y&0\\1&2\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}5&6\\1&8\end{array}} \right]$

$\Rightarrow$ $\left[ {\begin{array}{cccccccccccccccccccc}2&6\\0&{2x}\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}y&0\\1&2\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}5&6\\1&8\end{array}} \right]$

$\Rightarrow$ $\left[ {\begin{array}{cccccccccccccccccccc}{2 + y}&6\\1&{2x + 2}\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}5&6\\1&8\end{array}} \right]$

$\Rightarrow$ 2 + y = 5 and 2x + 2 = 8

$\Rightarrow$ y = 3 and x = 3

Hence, x = 3 and y = 3.