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

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

So, $6A=6\left(\begin{array}{cc}4& -2\\ 5& -9\end{array}\right)=\left(\begin{array}{cc}24& -12\\ 30& -54\end{array}\right)$

And $3B=3\left(\begin{array}{cc}8& 2\\ -1& -3\end{array}\right)=\left(\begin{array}{cc}24& 6\\ -3& -9\end{array}\right)$

$6A-3B=\left(\begin{array}{cc}24& -12\\ 30& -54\end{array}\right)-\left(\begin{array}{cc}24& 6\\ -3& -9\end{array}\right)=\left(\begin{array}{cc}24-24& -12-6\\ 30+3& -54+9\end{array}\right)$

$\therefore$ $6A-3B=\left(\begin{array}{cc}0& -18\\ 33& -45\end{array}\right)$