Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
![A = \left[\begin{array}{ccc} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \\\end{array}\right]](https://tex.z-dn.net/?f=A+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D+3+%26amp%3B+3+%26amp%3B+-1+%5C%5C+-2+%26amp%3B+-2+%26amp%3B+1+%5C%5C+-4+%26amp%3B+-5+%26amp%3B+2+%5C%5C%5Cend%7Barray%7D%5Cright%5D "A = \left[\begin{array}{ccc} 3 & 3 & -1 \\ -2 & -2 & 1 \\ -4 & -5 & 2 \\\end{array}\right]")
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Let A = , then A' = Now, A + A' = + = Let P = 1/2 ( A + A' ) = 1/2 = Now, P' = = P Thus, P = 1/2 ( A + A' ) is a symmetric matrix.Now, A - A' = - = is ur ans
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