Express the following matrices as the sum of a symmetric and a skew symmetric matrix: [(3, 3,-1) (-2, -2, 1) (-4, -5, 2)]

Question

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

\(\begin{vmatrix}3&3&-1\\-2&-2&1\\-4&-5&2\end{vmatrix}\)

[(3, 3,-1) (-2, -2, 1) (-4, -5, 2)] 

Answer 1

A square matrix A can be expressed as the sum of a symmetric and a skew symmetric matrix as

A = 1/2 (A + A^T) + 1/2 (A – A^T)