Diagonalize the matrix `A=[[3,-1,1],[-1,5,-1],[1,-1,3]]`

(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.

Find the rank of the matrix A = [[1,2,-1,3],[3,-1,2,1],[2,-2,3,2],[1,-1,1,-1]]

Using elementary transformations, find the inverse of the matrix [[-1,1,2],[1,2,3],[3,1,1]]

Find the rank of the matrix A = [[1,-1,1,-4],[3,-1,1,6],[4,-1,2,7],[2,-1,1,9]]

find the rank of matrix A=[[2,-1,-2,-4],[1,3,-1,-1],[3,1,-1,-1],[6,3,0,-7]]

Find the rank of the matrix [[1,2,3],[3,2,1],[1,3,2],[2,1,3]]

Find the rank of matrix.A= [[3,1,2,0],[1,0,-1,0],[2,1,3,0]]

Fiven the matrix A= [[-1,3,5],[1,-3,-5],[-1,3,5]] and X be the solution set of the equation A^(x)=A, where x in N -{1} . Evaluate prod((x^(3)+1)/(x^(3)-1)) where the contincued extends for all x in X .

Find the Rank of the matrix A = [[1,4,5,2],[2,1,3,0],[-1,3,2,2]]

Using elementary transformations, find the inverse of the matrix [[2, 0,-1],[ 5, 1, 0],[ 0, 1 ,3]]