Question

If $A=\left(\begin{array}{cc}4& -2\\ 5& -9\end{array}\right)$ and $B=\left(\begin{array}{cc}8& 2\\ -1& -3\end{array}\right)$, find $6A-3B$

Answer 1

Given, $A=\left(\begin{array}{cc}4& -2\\ 5& -9\end{array}\right),B=\left(\begin{array}{cc}8& 2\\ -1& -3\end{array}\right)$
$\Rightarrow 6A=6\left(\begin{array}{cc}4& -2\\ 5& -9\end{array}\right)=\left(\begin{array}{cc}24& -12\\ 30& -54\end{array}\right)$
$\Rightarrow -3B=-3\left(\begin{array}{cc}8& 2\\ -1& -3\end{array}\right)+\left(\begin{array}{cc}-24& -6\\ 3& 9\end{array}\right)$
Therefore, $6A-3B=\left(\begin{array}{cc}24-24& -12-6\\ 30+3& -54+9\end{array}\right)=\left(\begin{array}{cc}0& -18\\ 33& -45\end{array}\right)$