Question

If $A=\left[\begin{array}{cc}2& 5\\ 4& 4\end{array}\right],B=\left[\begin{array}{cc}0& 5\\ 1& 6\end{array}\right]$, find $5A^{\prime }+3B^{\prime }$

Answer 1

$A=\left[\underset{4}{2}\underset{4}{5}\right]$ $B=\left[\underset{1}{0}\underset{6}{5}\right]$

$A^T=\left[\underset{5}{2}\underset{4}{4}\right]$ (Transposing is inter changing the rows & columns)

$B^T=\left[\underset{5}{0}\underset{6}{1}\right]$

$\therefore$ $5A^T+{3B}^T$

$=5\left[\underset{5}{2}\underset{4}{4}\right]+3\left[\underset{5}{0}\underset{6}{1}\right]$

$=\left[\underset{25}{10}\underset{20}{20}\right]+\left[\underset{15}{0}\underset{18}{3}\right]$

$=\left[\underset{40}{10}\underset{38}{23}\right]$