$A = \begin{bmatrix}3 & 5 \\ 1 & -2\end{bmatrix}$ is written as $P + Q$, with $P$ symmetric and $Q$ skew-symmetric. What is $P$?

Explanation

1. 01

   $P = \frac{1}{2}(A + A')$ and $Q = \frac{1}{2}(A - A')$.

2. 02

   $A + A' = \begin{bmatrix}6 & 6 \\ 6 & -4\end{bmatrix}$, so $P = \begin{bmatrix}3 & 3 \\ 3 & -2\end{bmatrix}$.