If A = [1-253],B=[1-34-7] , then find the matrix A − 2B + 6I, where I is the unit matrix of order 2.

Exercise 2.2 | Q 2 | Page 46

QUESTION

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

SOLUTION

A – 2B + 6I = ${\displaystyle \left[\begin{array}{cc}1& -2\\ 5& 3\end{array}\right] 2\left[\begin{array}{cc}1& -3\\ 4& -7\end{array}\right]+6\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}1& -2\\ 5& 3\end{array}\right]-\left[\begin{array}{cc}2& -6\\ 8& -14\end{array}\right]+\left[\begin{array}{cc}6& 0\\ 0& 6\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}1-2+6& -2+6+0\\ 5-8+0& +14+6\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}5& 4\\ -3& 23\end{array}\right]}$.