Question

Any square matrix can be expressed as a sum of symmetric and skew-symmetric matrix.

(a) True

(b) False

The question was posed to me in a national level competition.

The doubt is from Symmetric and Skew Symmetric Matrices topic in chapter Matrices of Mathematics – Class 12

Answer 1

Correct answer is (a) True

For explanation: The given statement is true. Every square matrix can be expressed as a sum of sum of symmetric and skew-symmetric matrix.

If A is a square matrix then it can be expressed as

A = \(\frac{1}{2}\)(A+A’)+\(\frac{1}{2}\)(A-A’), where (A+A’) is symmetric and (A-A’) is skew-symmetric.