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

Express the matrix A as the sum of a symmetric matrix and a skew-symmetric matrix, where A=[(2,4,-6),(7,3,5),(1,-2,4)]

If A=[(1,5),(6,7)] , verify that A+A' is a symmetric matrix and A-A' is a skew-symmetric matrix.

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

If [(1,2,-1),(x,3,y),(-1,6,4)] is a symmetric matrix, then find x and y

If A=[(2,3),(1,0)]=P+Q , where P is symmetric and Q is skew-symmetric, then find the matrix P.

Prove that a matrix which is symmetric as well as skew-symmetric is a null matrix.

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

If A and B are symmetric matrices, then prove that AB +BA is a symmetric matrix.

Let A=[a_(ij)] is a square matrix of order 2 where a_(ij)=i^(2)-j^(2) . Then A is (i) Skew - symmetric matrix (ii) Symmetric matrix (iii) Diagonal matrix (iv) None of these

Prove that the diagonal elements of a skew-symmetric matrix are all zero