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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((ABC)/2) +tr((A(BC)^2)/4)+tr((A(BC)^3)/8)+.......+oo` is
(A) `6` (B) `9` (C) `12` (D) none of these

A

6

B

9

C

12

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`BC=[(3,4),(2,3)][(3,-4),(-2,3)]impliesB=[(1,0),(0,1)]`
`implies tr(A)+tr((ABC)/2)+tr((A(BC)^(2))/4)+tr ((A(BC)^(3))/8)+...+ oo`
`=tr (A)+tr (A/2)+tr (A/2^(2))+...`
`=tr (A)+1/2 tr (A)+1/2^(2) tr (A)...`
`=(tr (A))/(1-(1//2))`
`=2tr (A)=2(2+1)=6`
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