Express the matrix `A = [{:(4, 2,-1),(3,5,7),(1,-2,1):} ] ` as the sum of a symmetric and a skew-symmetric matrix.

Explanation

To express the matrix \( A = \begin{pmatrix} 4 & 2 & -1 \\ 3 & 5 & 7 \\ 1 & -2 & 1 \end{pmatrix} \) as the sum of a symmetric and a skew-symmetric matrix, we can follow these steps:

### Step 1: Define the symmetric and skew-symmetric matrices
A symmetric matrix \( S \) satisfies the condition \( S = S^T \) (i.e., it is equal to its transpose), while a skew-symmetric matrix \( K \) satisfies \( K = -K^T \) (i.e., its transpose is the negative of itself).

### Step 2: Use the formula to express \( A \)
We can express the matrix \( A \) as:
\[
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