1.

if A = [[cos theta, sin theta],[-sin theta, cos theta]] where theta = (2pi)/(7) then sum_(r=1)^(6) A^(r) =

Answer»

`[[1,0],[0,1]]`
`[[3,0],[0,3]]`
`[[-1,0],[0,-1]]`
NONE of these

Solution :`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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