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Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where 

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

A = [(3,-1,0)(2,0,3)(1,-1,2)]

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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

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