Express the following matrices as the sum of a symmetric and a skew symmetric matrix:(i) `[[3, 5],[ 1,-1]]` (ii) `[[6,-2, 2],[-2, 3,-1],[ 2,-1, 3]]` (iii) `[[3, 3,-1],[-2,-2, 1],[ -4,- 5, 2]]` (iv) `[[1 ,5],[-1, 2]]`

Explanation

To express the given matrices as the sum of a symmetric matrix and a skew-symmetric matrix, we can use the following formulas:

1. **Symmetric Matrix (P)**: \( P = \frac{1}{2}(A + A^T) \)
2. **Skew-Symmetric Matrix (Q)**: \( Q = \frac{1}{2}(A - A^T) \)

Where \( A^T \) is the transpose of matrix \( A \).

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