Show that the following matrices are skew symmetric: `[[0,1,-1],[-1,0,1],[1,-1,0]]`

Show that the following matrices are skew symmetric: [[0,e,f],[-e,0,g],[-f,-f,0]]

Expressing the following matrices as the sum of a symmetric and skew symmetric matrix : [[2,-2,-4],[-1,3,4],[1,-2,-3]]

Expressing the following matrices as the sum of a symmetric and skew symmetric matrix : [[1,2,4],[6,8,1],[3,5,7]]

(i) Show that the matrix A=[[1,-1, 5],[-1, 2, 1],[ 5, 1, 3]] is a symmetric matrix. (ii) Show that the matrix A=[[0, 1,-1],[-1, 2, 1],[ 1,-1, 0]] is a skew symmetric matrix.

Show that the following points are coplanar: (0,\ -1,\ 0),\ (2,\ 1,\ -1),\ (1, ,1\ ,1)a n d\ (3,\ ,3\ 0)dot

Which of the following matrices have eigen values as 1 and -1 ? (a) [(0,1),(1,0)] (b) [(0,1),(1,0)] (c) [(1,0),(0,-1)] (d) [(1,0),(0,1)]

Show that [[1,1],[0,1]]^2 = [[1,3],[0,1]]

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:(i) [[3, 5],[ 1,-1]] (ii) [[6,-2, 2],[-2, 3,-1],[ 2,-1, 3]] (iii) [[3, 3,-1],[-2,-2, 1],[ 4, 5, 2]] (iv) [[1 ,5],[-1, 2]]

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

Evaluate the following : [[1, 1, 1]] [[1,0,0],[0,1,0],[0,0,1]][[4],[4],[4]]