7*[[1,2,3],[0,2,4],[0,0,5]]

Find products : [[1,2,3],[4,5,6],[7,8,9]][[0,0,0],[0,0,0],[0,0,0]]

" (b) Find the rank of the matrix : "A=[[2,1,4,7],[3,6,2,1],[0,0,1,5]]

(a) Find the rank of the matrix [[2,1,4,7],[3,6,2,1],[0,0,1,5]]

Write the following as a single matrix: [1,-2,3] [[2,-1,5], [0,2,4],[-7,5,0]] -[2,-5,7]

If A=[[1,0,5],[3,2,7],[5,4,8]],B=[[3,1,2],[9,0,-6],[7,4,1]],C=[[2,0,-1],[7,5,6],[1,1,4]] , verify that A+(B+C)=(A+B)+C

If A= [3,2,0],[1,4,0][0,0,5] , then show that A^2 −7A+10I3 =0

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]]

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]]

Solve: 2X+Y+[[-2,1,3],[5,-7,3],[4,5,4]]=0,X-Y=[[4,7,0],[-1,2,-6],[-2,8,-5]] .

If A=[(1,2,3),(0,-4,2),(0,0,7)] , for what values of x, the matrix A-xI_3 is singular?