# Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = [(3,-1,0)(2,0,3)(1,-1,2)].

235 views
in Matrices
closed

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)]

+1 vote
by (31.5k points)
selected by

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