Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
![A = \left[\begin{array}{ccc} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \\\end{array}\right]](https://tex.z-dn.net/?f=A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D+6+%26amp%3B+-2+%26amp%3B+2+%5C%5C+-2+%26amp%3B+3+%26amp%3B+-1+%5C%5C+2+%26amp%3B+-1+%26amp%3B+3+%5C%5C%5Cend%7Barray%7D%5Cright%5D "A = \left[\begin{array}{ccc} 6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \\\end{array}\right]")
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