Q6 of 307 Page 6

Define a symmetric matrix. Prove that for is a symmetric matrix where A^T is the transpose of A.

A square matrix ‘A’ is called a symmetric matrix, if A = A^T.

Here,

From equation (i) and (ii),

So, A + A^T is a symmetric matrix.

Let Find matrices X and Y such that X + Y = A, where X is a symmetric and Y is a skew symmetric matrix.

Express the matrix as the sum of a symmetric and a skew-symmetric matrix.

Express the matrix as the sum of a symmetric and skew-symmetric matrix and verify your result.

Define a symmetric matrix. Prove that for is a symmetric matrix where AT is the transpose of A.