Question

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

(i) [(3, 3, - 1), (-2, -2, 1), (-4, -5, 2)]

(iI) [(1, 5), (-1, 2)]

Answer 1

(i)

where, P = 1/2(A + A') and Q = 1/2(A - A')

Thus P = 1/2(A + A')  is a symmetric matrix.

Thus Q = 1/2(A - A') is a skew symmetric matrix.

Representing A as the sum of P and Q,

Thus P = 1/2(A + A') is a symmetric matrix.

Thus Q = 1/2(A - A')  is a skew symmetric matrix.

Representing A as the sum of P and Q,