Express the matrix `[(7,1,5),(-4,0,3),(-2,6,1)]`as the sum of a symmetric and a skew symmetric matrices.

Explanation

`A = [[1,3,5],[-6,8,3],[-4,6,5]]`

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

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

Here, `A^T = [[1,-6,-4],[3,8,6],[5,3,5]]`

`:.` Symmetric matrix `=1/2[[2,-3,1],[-3,16,9],[1,9,10]]`

`:.` Skew-symmetric matrix `= 1/2[[0,9,9],[-9,0,-3],[-9,3,0]]`

`:. A = 1/2[[2,-3,1],[-3,16,9],[1,9,10]]+1/2[[0,9,9],[-9,0,-3],[-9,3,0]]`