If $A' = \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&3\\1&2\end{array}} \right]$and $B = \left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&0\\1&2\end{array}} \right]$, then find $(A + 2B)'$.

.:

$A' = \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&3\\1&2\end{array}} \right]$ $\Rightarrow$ $A = \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&1\\3&2\end{array}} \right]$,$B$

$= \left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&0\\1&2\end{array}} \right]$
$\therefore$ $A + 2B = \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&1\\3&2\end{array}} \right] + 2\left[ {\begin{array}{cccccccccccccccccccc}{ - 1}&0\\1&2\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&1\\3&2\end{array}} \right] + \left[ {\begin{array}{cccccccccccccccccccc}{ - 2}&0\\2&4\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}{ - 2 - 2}&{1 + 0}\\{3 + 2}&{2 + 4}\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}{ - 4}&1\\5&6\end{array}} \right]$

Hence, $(A + 2B)' = \left[ {\begin{array}{cccccccccccccccccccc}{ - 4}&5\\1&6\end{array}} \right]$