Let $A = \begin{bmatrix} 3 & 2 & 5 \\[0.3em] 4 & 1 & 3 \\[0.3em] 0 & 6 & 7 \end{bmatrix}$ Express $A$ as sum of two matrices such that one is symmetric and the other is skew symmetric.

Question

$\begin{array}{1 1}B=\begin{bmatrix} 3 & 3 & \frac{5}{2} \\ 3 & 1 & \frac{9}{2} \\ \frac{5 }{2} & \frac{9}{2} & 7 \end{bmatrix} C = \begin{bmatrix} 0 & -1 & \frac{5}{2} \\ 1 & 0 & \frac{-3}{2} \\ \frac{-5 }{2} & \frac{3}{2} & 0 \end{bmatrix} \\ B=\begin{bmatrix} 3 & 3 & \frac{5}{2} \\ 3 & 2 & \frac{9}{3} \\ \frac{5 }{2} & \frac{9}{2} & 7 \end{bmatrix} C = \begin{bmatrix} 0 & 1 & \frac{5}{2} \\ -1 & 0 & \frac{-3}{2} \\ \frac{-5 }{2} & \frac{3}{2} & 0 \end{bmatrix} \\ B=\begin{bmatrix} 3 & 3 & \frac{5}{2} \\ 3 & 1 & \frac{9}{2} \\ \frac{5 }{2} & \frac{9}{2} & 7 \end{bmatrix} C = \begin{bmatrix} 1 & -1 & \frac{5}{2} \\ 1 & 1 & \frac{-3}{2} \\ \frac{-5 }{2} & \frac{3}{2} & 0 \end{bmatrix} \\ B=\begin{bmatrix} 1 & 1 & \frac{5}{2} \\ 2 & 1 & \frac{9}{2} \\ \frac{5 }{2} & \frac{9}{2} & 7 \end{bmatrix} C = \begin{bmatrix} 0 & -1 & \frac{5}{2} \\ 1 & 0 & \frac{-3}{2} \\ \frac{-5 }{2} & \frac{3}{2} & 0 \end{bmatrix}\end{array}$