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Question
If A=[cosθsinθsinθ−cosθ],B=[10−11],C=ABAT,then ATCnA equals to(nϵZ+)
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Solution
The correct option is D [10−n1]
A=[cosθsinθsinθ−cosθ]AAT=I (i)Now,C=ABAT⇒ATC=BAT (ii)Now ATCnA=ATC.Cn−1A=BATCn−1A(from(ii))=BATC.Cn−2A=B2ATCn−2A=.......=Bn−1ATCA=Bn−1BATA=Bn=[10−n1]
A=[cosθsinθsinθ−cosθ]AAT=I (i)Now,C=ABAT⇒ATC=BAT (ii)Now ATCnA=ATC.Cn−1A=BATCn−1A(from(ii))=BATC.Cn−2A=B2ATCn−2A=.......=Bn−1ATCA=Bn−1BATA=Bn=[10−n1]
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