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

Explanation

To express the matrix \( B = \begin{pmatrix} 2 & -2 \\ -1 & 3 \end{pmatrix} \) 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 property \( S^T = S \), while a skew-symmetric matrix \( K \) satisfies \( K^T = -K \).

### Step 2: Use the formula for decomposition
We can express the matrix \( B \) as the sum of a symmetric matrix and a skew-symmetric matrix using the following formulas:
\[
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