Find the symmetric and the skew-symmetric such that the sum of the matrices is 

Concept: 

A matrix X can be written as a sum of the symmetric and skew-symmetric matrix which are 

P(symmetric) = (X + XT)

Q(skew-symmetric) = (X - XT)

Where XT is transpose of matrix X

Given matrix X = 

Transpose matrix X^T = 

Symmetric matrix (P) =  (X + XT)

⇒ P =  

⇒ P =  

⇒ P = 

Skew-symmetric matrix (Q) = (X - XT)

⇒ Q =  

⇒ Q =  

⇒ Q =