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# If $A = \begin{bmatrix} 3 & 4 \\ 2 & 3 \end{bmatrix}$, find A + A', where A' is the transpose of matrix A.

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• The transpose can be obtained by changing the rows and columns
$A=\begin{bmatrix}3 & 4\\2 & 3\end{bmatrix}$
$A'=\begin{bmatrix}3 & 2\\4 & 3\end{bmatrix}$
$A+A'=\begin{bmatrix}3 & 4\\2 & 3\end{bmatrix}+\begin{bmatrix}3 & 2\\4 & 3\end{bmatrix}$
$\Rightarrow \begin{bmatrix}3+3 & 4+2\\2+4 & 3+3\end{bmatrix}$
$\Rightarrow \begin{bmatrix}6 & 6\\6 & 6\end{bmatrix}$
answered Mar 28, 2013