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

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

Prove that A+A^T is symmetric and A-A^T is skew symmetric matrix, where A=[[1,2,4],[3,2,1],[-2,-3,2]]

Prove that A+A^T is symmetric and A-A^T is skew symmetric matrix, where A=[[5,2,-4],[3,-7,2],[4,-5,-3]]

For each of the following matrices,using its transpose state whether it is a symmetric,a skew-symmetricor neither. [[1,2,-5],[2,-3,4],[-5,4,9]]

For each of the following matrices,using its transpose,state whether it is a symmetric or a skew-symmetric or neither. [[2,5,1],[-5,4,6],[-1,-6,3]]

For each of the following matrices,using its transpose state whether it is a symmetric,a skew-symmetric or neither. [[0,1+2i,i-2],[-1-2i,0,-7],[2-i,7,0]]

Classify the following matrices as a row, a column,a square, a diagonal,a scalar,a unit,an upper triangular,a lower triangular,a symmetric or a skew-symmetric matrix. [[2,0,0],[3,-1,0],[-7,3,1]]