Fill
`|A|=[[1,2,3],[1,1,5],[2,4,7]]=1|[...,...],[...,...]|-2|[...,...],[...,...]|+3|[...,...],[...,...]|`

If A=[[1,2,3],[3,1,2],[2,3,1]] and B=[[-5,7,1],[1,-5,7],[7,1,-5]] prove that AB=18I_3

Evaluate the following : [[1,2,-3],[-2,1,7]] [[2,3,1],[5,4,2],[1,6,3]]

The inverse of [[3,5,7],[2,-3,1],[1,1,2]] is

If =[[2,3,4],[1,2,3],[4,-5,7]], B= [[2,5,-1],[3,-1,2],[7,2,-3]] , verify that (A+B)'=A'+B'

Show that(i) [[5,-1],[ 6 ,7]][[2, 1],[ 3 ,4]]!=[[2, 1],[ 3, 4]][[5,-1],[ 6, 7]] (ii) [[1, 2, 3],[ 0, 1, 0],[ 1, 1, 0]][[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]]!=[[-1, 1, 0],[ 0,-1, 1],[ 2, 3, 4]][[1 ,2 ,3],[ 0, 1, 0],[ 1, 1, 0]]

If A = [(2,2,1), (1,3,1), (1,2,2)] then A^-1+(A-5I) (AI)^2 = (i) 1/ 5 [[4,2, -1], [-1,3,1], [-1,2,4]] (ii) 1/5 [[4, -2, -1], [-1, 3, -1], [-1, -2,4]] (iii) 1/3 [[4,2, -1], [-1,3,1], [-1,2,4]] (iv) 1/3 [[4, -2, -1], [-1,3, -1], [-1, -2,4]]

4.Find the rank of the matrix [[3,4,1,2],[3,2,1,4],[7,6,2,5]]

4.Find the rank of the matrix [[3,4,1,2],[3,2,1,4],[7,6,2,5]]

Find the values of following determinants. (1) |[-1,7],[2,4]| (2) |[5,3],[-7,0]| (3) |[7/3,5/3],[3/2,1/2]|

If A={1,2,3} and B={1,3,5,7}, then A uu B={1,2,3,5,7}