Prove that square matrix can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix.

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

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

Statement 1: Matrix 3xx3,a_(i j)=(i-j)/(i+2j) cannot be expressed as a sum of symmetric and skew-symmetric matrix. Statement 2: Matrix 3xx3,a_(i j)=(i-j)/(i+2j) is neither symmetric nor skew-symmetric

Express the matrix A =[[7,1,5],[-4,0,3],[-2,6,1]] as the sum of a symmetric and a skew-symmetric matrices.

If A is symmetric as well as skew-symmetric matrix, then A is

Express the matrix [(7,1,5),(-4,0,3),(-2,6,1)] as the sum of a symmetric and a skew symmetric matrices.

Express the matrix A=[(1,3,5),(-6,8,3),(-4,6,5)] as the sum of a symmetric and a skew - symmetric matrices.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix, (ii) A -A^T is a skew-symmetric matrix and (iii) AA^T and A^TA are symmetric matrices.

Express [(3,2,-4),(4,2,-3),(0,5,1)] as sum of symmetric and skew symmetric matrix.

Prove that inverse of a skew-symmetric matrix (if it exists) is skew-symmetric.