Express the matrix `A=[4 2-1 3 5 7 1-2 1]` as the sum of a symmetric and a skew-symmetric matrix.

Explanation

A matrix `A` can be expressed as the sum of symmetric and skew-symmetric matrix in following way:
`A = 1/2(A+A^T)+1/2(A-A^T)`

Here,

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

`:. A^T = [[4,3,1],[2,5,-2],[-1,7,1]]`

`=>A+A^T = [[4,2,-1],[3,5,7],[1,-2,1]]+ [[4,3,1],[2,5,-2],[-1,7,1]] = [[8,5,0],[5,10,5],[0,5,2]]`

`=>A-A^T = [[4,2,-1],[3,5,7],[1,-2,1]]- [[4,3,1],[2,5,-2],[-1,7,1]] = [[0,-1,-2],[1,0,9],[2,-9,0]]`

`:. A = 1/2[[8,5,0],[5,10,5],[0,5,2]]+1/2[[0,-1,-2],[1,0,9],[2,-9,0]]`

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