Express the matrix `[3-2-4 3-2-5-1 1 2]` as the sum of a symmetric and skew-symmetric matrix and verify your result.

Explanation

Given:`[(3,-2,-4),( 3,-2,-5),(-1, 1, 2)]`

Then

`A^T=[(3,3,-1),( -2,-2,-1),(-4,-5,2)]`

Now A can be written as sum of a symmetric and skew symmetric matrix,

`A=1/2(A+A^T)+1/2(A-A^T)`

Let`P=1/2(A+A^T)`

`P=1/2{[(3,-2,-4),( 3,-2,-5),(-1,1,2)]+[(3,3,-1),( -2,-2,1),(-4,-5,2)]}`

`P=1/2[(6,1,-5),(1,-4,-4),(-5,-4,4)]`

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