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Question
If A= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.
Solution
`A=[(3,5),(7,9)]`
P is symmetric matrix. So, `P = 1/2(A+A^T)`
Q is skew symmetric matrix. So, `Q=1/2(A-A^T)`
`A^T=[(3,7),(5,9)]`
`P=1/2[(6,12),(12,18)]=[(3,6),(6,9)]`
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