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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. - Mathematics

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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.

 

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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)]`

Concept: Symmetric and Skew Symmetric Matrices
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