Question

given : $M=\left[\begin{array}{cc}5& -3\\ -2& 4\end{array}\right]$
Find its transopose
Matrix M ' If possible, find:
(i) M + M ' (ii) M - M '

Answer 1

given :$M=\left[\begin{array}{cc}5& -3\\ -2& 4\end{array}\right]$

Matrix $M^{\prime }=\left[\begin{array}{cc}5& -2\\ -3& 4\end{array}\right]$

(i) M + M ' = ​​$\left[\begin{array}{cc}5+5& -3-2\\ -2-3& 4+4\end{array}\right]$ = $\left[\begin{array}{cc}10& -5\\ -5& 8\end{array}\right]$​​​​​​​

(ii) M - M ' = ​​$\left[\begin{array}{cc}5-5& -3+2\\ -2+3& 4-4\end{array}\right]$​​​​​​​ = ​​$\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$​​​​​​​