Let `A=[(3,2,5),(4,1,3),(0,6,7)]` Express `A` as sum of two matrices such that one is symmetric and the other is skew symmetric.

Explanation

`A = [[3,2,5],[4,1,3],[0,6,7]]`

Symmetric matrix can be given as `(A+A^T)/2`.

Skew-symmetric matrix can be given as `(A-A^T)/2`.

Here, `A^T = [[3,4,0],[2,1,6],[5,3,7]]`

`:.` Symmetric matrix `=1/2[[6,6,5],[6,2,9],[5,9,14]]`

`:.` Skew-symmetric matrix `= 1/2[[0,-2,5],[2,0,-3],[-5,3,0]]`

`:. A = 1/2[[6,6,5],[6,2,9],[5,9,14]]+1/2[[0,-2,5],[2,0,-3],[-5,3,0]]`