Question

If $A=\left[\begin{array}{cc}3& -4\\ 5& 2\end{array}\right]\&B=\left[\begin{array}{cc}1& 3\\ 5& 8\end{array}\right],$ then find $3A-5B+4I$.

Answer 1

$A=\left[\begin{array}{cc}3& -4\\ 5& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ 5& 8\end{array}\right],$

and I = $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$3A-5B+4I$

$=3\left[\begin{array}{cc}3& -4\\ 5& 2\end{array}\right]-5\left[\begin{array}{cc}1& 3\\ 5& 8\end{array}\right]+4\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

$=\left[\begin{array}{cc}9& -12\\ 15& 6\end{array}\right]-\left[\begin{array}{cc}5& 15\\ 25& 40\end{array}\right]+\left[\begin{array}{cc}4& 0\\ 0& 4\end{array}\right]$

$=\left[\begin{array}{cc}13& -12\\ 15& 10\end{array}\right]-\left[\begin{array}{cc}5& 15\\ 25& 40\end{array}\right]$

$=\left[\begin{array}{cc}8& -27\\ -10& -30\end{array}\right]$