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If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] an...

If `P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]]` and `A=[[1,1] , [0,1]]` and `Q=PAP^T` and `x=P^TQ^(2005)P` then x is equal to

A

`[(1,2005),(0,1)]`

B

`[(sqrt(3)//2,2005),(1,0)]`

C

`[(1,2005),(sqrt(3)//2,1)]`

D

`[(1,sqrt(3)//2),(0,2005)]`

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A
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DISHA PUBLICATION-MATRICES-Exercise 2: Concept Applicator
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  8. IfA^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(...

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  12. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

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  13. [{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}] then the value of x,...

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  14. Given that [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega...

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  15. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then te value of alpha f...

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  19. Find the value of k so that A^2=8A+kI where A=[(1,0),(-1,7)].

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  20. A square matrix P satisfies P^(2)=I-P where I is identity matrix. If P...

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