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If [(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (...

If `[(cos\ (2pi)/7,-sin\ (2pi)/7),(sin\ (2pi)/7,cos\ (2pi)/7)]^k=[(1,0),(0,1)],` then the least positive integral value of `k`, is

A

3

B

6

C

7

D

14

Text Solution

Verified by Experts

The correct Answer is:
C
We know that `[(cos theta,- sin theta),(sin theta,cos theta)]^(n)=[(cos n theta,-sin n theta),(sin n theta,cos n theta)]`
`:. [("cos" (2pi)/7,-"sin" (2pi)/7),("sin"(2pi)/7,"cos"(2pi)/7)]^(k)=[("cos"(2kpi)/7,-"sin"(2kpi)/7),("sin" (2kpi)/7,"cos" (2kpi)/7)]`
`=[(1,0),(0,1)]`, if `k=7m`, where `m in N`
Hence, the least value of k is 7.
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