Express the matrix [(2,3,1),(1,-1,2),(4,1,2)] as the sum of a symmetric and a skew symmetric matrix. ​

Question

Express the matrix \(\begin{bmatrix} 2 & 3 & 1 \\[0.3em] 1 & -1 & 2 \\[0.3em] 4 & 1 & 2 \end{bmatrix}\) as the sum of a symmetric and a skew symmetric matrix.

Answer 1

If A is any matrix then it can be written as the sum of a symmetric and skew symmetric matrix.

Symmetric matrix is given by 1/2(A + A’)

Skew symmetric is given by 1/2(A – A’)

And A = 1/2(A + A’) + 1/2(A – A’)