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Prove that: 2cos frac (pi)(13)cos frac (...

Prove that: `2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+cos frac (5pi)(13)=0`

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The correct Answer is:
B
We have, `P^(T) = P^(-1) " " [ because PP^(T) =I]`
Now, ,,`Q= PAP^(T) = PAP^(-1)`
`therefore Q^(2007) = PA^(2007) P^(-1) `
`therefore P^(T) Q^(2007 ) P= P^(-1) (PA^(2007)P^(-1)) P`
`= A^(2007 = [[1,2007],[0,1]][becauseA^(2)=[[1,2],[0,1]],A^(3) = [[1,3],[0,1]],...]`
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ARIHANT MATHS-MATRICES -Exercise (Single Option Correct Type Questions)
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  6. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

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  7. Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+co...

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  12. If A=[[cos theta , sin theta],[sin theta,-costheta]], B = [[1,0],[-1,1...

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  13. If A is a square matrix of order 3 such that abs(A)=2, then abs((adj...

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  14. If A and B are different matrices satisfying A^(3) = B^(3) and A^(2)...

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  15. Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]

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  16. If A = [[a,b,c],[x,y,z],[p,q,r]], B= [[q , -b,y],[-p,a,-x],[r,-c,z]] a...

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  17. Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4)...

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