If `A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)]` is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is (a) `[(2, 2,-4 ),(2, 3, 4),(-4, 4, 2)]` (b) `[(2, 4,-5),( 0, 3, 7),(-3, 1, 2)]` (c) `[(4, 4,-8),( 4, 6, 8),(-8, 8, 4)]` (d) `[(1, 0 ,0 ),(0 ,1 ,0),( 0, 0, 1)]`

Explanation

We have given:`A=[(2, 0,-3),( 4, 3, 1),(-5, 7, 2)]`

Then

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

Now any matrix can be expressed as the sum of a symmetric and skew-symmetric matrix

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

`implies A=P+Q`

Then `P=1/2(A+A^T)=1/2([(2, 0,-3),( 4, 3, 1),(-5, 7, 2)]+[(2, 4,-5),( 0, 3, 7),(-3, 1, 2)] )`

`implies P=[(2,2,-4),(2,3,4),(-4,4,2)]`