Question:
If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$, find $A+A^{\top}$
Solution:
Given : $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]$
$A^{T}=\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]$
$A+A^{T}=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]+\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right]$
$\Rightarrow A+A^{T}=\left[\begin{array}{ll}1+1 & 2+3 \\ 3+2 & 4+4\end{array}\right]$
$\Rightarrow A+A^{T}=\left[\begin{array}{ll}2 & 5 \\ 5 & 8\end{array}\right]$