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If A=[[cos theta,sin theta],[-sin theta,...

If A=`[[cos theta,sin theta],[-sin theta,cos theta]], ` then `lim _(n rarr infty )A^(n)/n ` is (where `theta in R`)

A

`[[1,0],[0,1]]`

B

`[[3,0],[0,3]]`

C

`[[-1,0],[0,-1]]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`A + A^(2) + A^(3) + A^(4) + A^(5) + A^(6)`
`=[[cos theta + cos 2 theta + cos 3 theta + cos 4 theta + cos 5 theta + cos 6 theta" "sin theta + sin 2 theta+ sin 3theta+ sin 4 theta + 5 sin theta + sin 6 theta],[-[sin theta + sin 2 theta + sin theta + sin 4 theta+ sin 5 theta+ sin 6theta]" " cos theta + cos 2 theta + cos 3 theta + cos 4 theta + cos 5 theta + cos 6 theta]]`
`=[[-1,0],[0,-1]]`
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