Chapter 2.2, Problem 34P

If $A$ is an $n\times n$ matrix, then the matrices $B$ and $C$ defined by

$B=\frac{1}{2}\left(A+A^T\right)$, $C=\frac{1}{2}\left(A-A^T\right)$

are referred to as the symmetric and skew symmetric parts of $A$ respectively. Problems 32-36 investigate properties of $B$ and $C$.

Find $B$ and $C$ for the matrix

$A=\left[\begin{array}{ccc}4& -1& 0\\ 9& -2& 3\\ 2& 5& 5\end{array}\right]$