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

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

" 3.Find the rank of the matrix "[[0,-1,2],[4,3,1],[4,2,3]]

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

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

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 : [[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 matrix A= [[1,2,-1,0],[0,1,3,1],[2,5,1,2]]