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

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

(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 [[1,2,3],[3,2,1],[1,3,2],[2,1,3]]

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

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

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

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 .

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

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

Find the rank of the matrix : [[-1,-3,3,-1],[1,1,-1,0],[2,-5,2,-3],[-1,1,0,1]]