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Question
If \[A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}\] , find A + AT.
Solution
\[Given: A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix} \]
\[ A^T = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}\]
\[A + A^T = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix} + \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}\]
\[ \Rightarrow A + A^T = \begin{bmatrix}1 + 1 & 2 + 3 \\ 3 + 2 & 4 + 4\end{bmatrix}\]
\[ \Rightarrow A + A^T = \begin{bmatrix}2 & 5 \\ 5 & 8\end{bmatrix}\]
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