Given A = \( \begin{bmatrix} 3 & -1 & 0 \\[0.3em] 2 & 0 & 3\\[0.3em] 1 &-1 & 2 \end{bmatrix}\), to express as sum of symmetric matrix P and skew symmetric matrix Q

A = P + Q

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

First we will find A’,

A' = \( \begin{bmatrix} 3 & 2 & 1\\[0.3em] -1 & 0 & -1\\[0.3em] 0 &3 & 2 \end{bmatrix}\)

**Now using above mentioned formulas,**

P = \(\frac{1}{2}\)(A + A')

Q = \(\frac{1}{2}\)(A - A')

Now A = P + Q