Question
Given $M=\left[\begin{array}{cc}5 & -3 \\ -2 & 4\end{array}\right]$ Find its transpose matrix $M^t$. If possible find $M+M^t$
✓
Answer
$M=\left[\begin{array}{cc}5 & -3 \\ -2 & 4\end{array}\right] $
$ M^t=\left[\begin{array}{cc}5 & -2 \\ -3 & 4\end{array}\right]$
$M+M^t=\left[\begin{array}{cc}5 & -3 \\ -2 & 4\end{array}\right]+\left[\begin{array}{cc}5 & -2 \\ -3 & 4\end{array}\right]$
$=\left[\begin{array}{cc}5+5 & -3-2 \\ -2-3 & 4+4\end{array}\right]$
$=\left[\begin{array}{cc}10 & -5 \\ -5 & 8\end{array}\right]$
$ M^t=\left[\begin{array}{cc}5 & -2 \\ -3 & 4\end{array}\right]$
$M+M^t=\left[\begin{array}{cc}5 & -3 \\ -2 & 4\end{array}\right]+\left[\begin{array}{cc}5 & -2 \\ -3 & 4\end{array}\right]$
$=\left[\begin{array}{cc}5+5 & -3-2 \\ -2-3 & 4+4\end{array}\right]$
$=\left[\begin{array}{cc}10 & -5 \\ -5 & 8\end{array}\right]$
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