Question

If $A=\left[\begin{array}{cc}3& -2\\ 5& 4\end{array}\right],B=\left[\begin{array}{cc}1& 4\\ 6& -7\end{array}\right]$, then find the matrix $A-4B+7I$, where I is the unit matrix of order 2.

Answer 1

$A=\left[\begin{array}{cc}3& -2\\ 5& 4\end{array}\right]$ $B=\left[\begin{array}{cc}1& 4\\ 6& -7\end{array}\right]$

$A-4B+71$

$\Rightarrow \left[\begin{array}{cc}3& -2\\ 5& 4\end{array}\right]-4\left[\begin{array}{cc}1& 4\\ 6& -7\end{array}\right]+7\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Where I is a $2\times 2$ unit matrix

$\Rightarrow \left[\begin{array}{cc}3& -2\\ 5& 4\end{array}\right]+\left[\begin{array}{cc}-4& -16\\ -24& 28\end{array}\right]+\left[\begin{array}{cc}7& 0\\ 0& 7\end{array}\right]$

(Using scalar multiplication of matrices)

$\Rightarrow \left[\begin{array}{cc}6& -18\\ -19& 39\end{array}\right]$.