Question

Given $A=\left[\begin{array}{cc}3& 1\\ -2& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}4& -3\\ 2& -1\end{array}\right]$

Find A+B-2l where l is a $2\times 2$ unit matrix

• A. $\left[\begin{array}{cc}5& 2\\ 0& 2\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}1& 1\\ 0& 0\end{array}\right]$
• D. $\left[\begin{array}{cc}5& -2\\ 0& -2\end{array}\right]$

Answer 1

The correct option is D

$\left[\begin{array}{cc}5& -2\\ 0& -2\end{array}\right]$

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

$2l=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$

$A+B-2l=\left[\begin{array}{cc}7& -2\\ 0& 0\end{array}\right]-\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]=\left[\begin{array}{cc}5& -2\\ 0& -2\end{array}\right]$