Diagonalize the matrix `[[1,-1,2],[0,2,-1],[0,0,3]]`

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

(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.

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

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

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]]

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

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

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

The matrix [{:(1,0,0),(0,2,0),(0,0,4):}] is a