Question

If $A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right]$, $B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$. Find $AB-5C$.

Answer 1

Given : $A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right]$, $B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$
$AB=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right]\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$
$=\left[\begin{array}{cc}0+35& 6+21\\ 0+20& 4+12\end{array}\right]=\left[\begin{array}{cc}35& 27\\ 20& 16\end{array}\right]$
$5C=5\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]=\left[\begin{array}{cc}5& -25\\ -20& 30\end{array}\right]$
$AB-5C=\left[\begin{array}{cc}35& 27\\ 20& 16\end{array}\right]-\left[\begin{array}{cc}5& -25\\ -20& 30\end{array}\right]$
$=\left[\begin{array}{cc}30& 52\\ 40& -14\end{array}\right]$