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If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]],...

If `P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]]` and `Q=PAP^T` and `X=P^TQ^(2005)P`, then `X` equal to:

A

`|{:(,1,2005),(,0,1):}|`

B

`|{:(,4+2005sqrt3,6015),(,2005,4-2005sqrt3):}|`

C

`(1)/(4)|{:(,2+sqrt3,1),(,-1,2-sqrt3):}|`

D

`(1)/(4)|{:(,2005,2-sqrt3),(,2+sqrt3,2005):}|`

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A
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RESONANCE-MATRICES & DETERMINANT-EXERCISE-2
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  2. If AB=0, then for the matrices A=[{:(cos^2theta,sinthetacostheta),(si...

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  3. If X=[{:(3,-4),(1,-1):}], then value of X^(n) is (where n is a natural...

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  4. If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

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  5. The number of nxxn matrix A and B such that AB - BA = I is. . .

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  6. If B, C are square matrices of order n and if A = B + C, BC = CB,C^2=0...

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  7. How many 3 x 3 skew symmetric matrices can be formed using numbers -2,...

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  8. If A is a skew-symmetric matrix and n is an even natural number,...

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  9. Number of 3 xx 3 non symmeteric matrix A such that A^(T)=A^(2)-I and |...

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  10. Matrix A is such that A^(2)=2A-I, where I is the identify matrix. Then...

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  11. If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]] and Q=PAP^T a...

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  12. Let Delta =|(sin theta cos phi, sin theta sin phi, cos theta), (cos th...

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  13. Delta =|(1+a^2+a^4,1+ab+a^2b^2, 1+ac+a^2c^2), (1+ab+a^2b^2, 1+b^2+b^4,...

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  14. If D=|{:(,a^(2)+1,ab,ac),(,ba,b^(2)+1,bc),(,ca,cb,c^(2)+1):}| then D=

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  15. Value of the Delta=|{:(,a^(3)-x,a^(4)-x,a^(5)-x),(,a^(5)-x,a^(6)-x,a^(...

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  16. If Delta1=|[2a,b,e],[2d,e,f],[4x,2y,2z]|,Delta2=|[f,2d,e],[2z,4x,2y],[...

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  17. From the matrix equation AB=AC, we conclude B=C provided.

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  18. Let A=|{:(,-2,7,sqrt3),(,0,0,-2),(,0,2,0):}| and A^(4)=lambda,I,"then"...

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  19. If A is 3 xx 3 square matrix whose characteristics polynomical equatio...

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  20. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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