Express the matrix `[3-2-4 3-2-5-1 1 2]` as the sum of a symmetric and 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 = [[3,-2,-4],[3,-2,-5],[-1,1,2]]`

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

`=>A+A^T = [[3,-2,-4],[3,-2,-5],[-1,1,2]]+[[3,3,-1],[-2,-2,1],[-4,-5,2]] = [[6,1,-5],[1,-4,-4],[-5,-4,4]]`

`=>A-A^T = [[3,-2,-4],[3,-2,-5],[-1,1,2]]-[[3,3,-1],[-2,-2,1],[-4,-5,2]] = [[0,-5,-3],[5,0,-6],[3,6,0]]`

`:. A = 1/2 [[6,1,-5],[1,-4,-4],[-5,-4,4]]+ [[0,-5,-3],[5,0,-6],[3,6,0]]`

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