Home
Class 12
MATHS
Consider three matrices A=[(2,1),(4,1)],...

Consider three matrices `A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4),(-2,3)].` Then the value of the sum `tr(A)+tr((A(BC))/2) +tr((A(BC)^2)/4)+tr((A(BC)^3)/8)+.......+oo` is (A) `6` (B) `9` (C) `12` (D) none of these

A

4

B

9

C

12

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
`because BC = [[3,4],[2,3]] [[3,-4],[-2,3]]=[[1,0],[0,1]]=I`
`therefore tr (A) + tr ((ABC)/2) + tr ((A(BC)^(2))/4) +tr((A(BC)^(3))/8) +...`
`= tr (A) + tr (A/2) + tr(A/2^(2))+tr(A/2^(3))+..." upto " infty`
`=tr (A) + 1/2 tr (A) + 1/2^(2) tr (A) + ... " upt0 " infty `
`= (tr(A))/(1-(1/2)) = 2 tr (A) = 2(2+1) = 6`
Promotional Banner

Similar Questions

Explore conceptually related problems

IF A={:|(3,4),(1,2)| find the value of 3|A|.

If A = [(4,-1),(0,3)], B = [(1,2),(-1,3)] and C = [(1, -2),(3,5)] verify that A(BC) = (AB)C .

If A = [(1,-1),(2,3)], B = [(1,3),(-1,4)] and C = [(2,-2),(3,0)] verify that A(BC) = (AB)C .

If A = [{:(1,2),(-2,3):}], B= [{:(2,1),(2,3):}] and C = [{:(-3,1),(2,0):}] ,verify that (AB)C = A(BC) and A(B+C)=AB+AC.

Let A=[(2,-1),(3,4)], B=[(5,2),(7,4)], C=[(2,5),(3,8)] . Find a matrix D such that CD=AB .

If A=((1,1,-1),(2,0,3),(3,-1,2)),B=[(1,3),(0,2),(-1,4)] and C=[(1,2,3,-4),(2,0,-2,1)] prove that (AB)C=A(BC)

If A=[(1,3),(4,2)],B=[(2,-1),(1,2)]," then "|ABB'|=

If A = [(2,2),(1,3)], B = [(2,0),(4,3)] and C = [(1,4),(1,3)] . Calculate AB, AC and A (B + C). Verify that AB + AC = A(B +C) .

If A= [(1,1,-1),(2,0,2),(3,-1,2)],B=[(1,3),(0,2),(-1,4)] and C = [(1,2,3,-4),(2,0,-2,1)] then find A(BC) and (AB) C. Show that A(BC) =(AB) C.

If A = [(1,3),(4,2)] , B = [(2,-1),(1,2)] , then |ABB'| =