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Question
`If A = ([3 5] , [7 9])` is written as A = P + Q, where as A = p + Q , Where P is a symmetric matrix and Q is skew symmetric matrix , then wqrite the matrix P.
Solution
P is symmetric matrix. So,
\[P = \frac{1}{2}\left( A + A^T \right)\]
Q is skew symmetric matrix. So,
\[A^T = \begin{bmatrix}3 & 7 \\ 5 & 9\end{bmatrix}\]
\[P = \frac{1}{2}\begin{bmatrix}6 & 12 \\ 12 & 18\end{bmatrix} = \begin{bmatrix}3 & 6 \\ 6 & 9\end{bmatrix}\]
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