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

Give an example of a matrix which is a lower triangular as well as upper triangular matrix.

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

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

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

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

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

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

Provide a term to radially symmetrical flowers.