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Expess the matrix A=[{:(2,0,-4),(-3,1,5...

Expess the matrix `A=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]` as a sum of symmetic and skew symmetric matrices.

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`A=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]`
`implies A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}][{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`A+A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]+[{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`=[{:(4,-3,0),(-3,2,3),(0,3,6):}]`
`implies (1)/(2)(A+A')=[{:(2,-3//2,0),(-3//2,1,3//2),(0,3//2,3):}]`
`and A-A'=[{:(2,0,-4),(-3,1,5),(4,-2,3):}]-[{:(2,-3,4),(0,1,-2),(-4,5,3):}]`
`=[{:(0,3,-8),(-3,0,7),(8,-7,0):}]`
`implies (1)/(2)(A-A')=[{:(0,3//2,-4),(-3//2,0,7//2),(4,-7//2,0):}]`
`Now A=(1)/(2)(A-A')+(1)/(2)(A-A')`
`implies [{:(2,0,-4),(-3,1,5),(4,-2,3):}]`
`=[{:(2,-3//2,0),(-3//2,1,3//2),(0,3//2,3):}]+[{:(0,3//2,-4),(-3//2,0,7//2),(4,-7//2,0):}].`
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