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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:

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CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let omega != 1 be cube root of unity and S be the set of all non-sing...

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  2. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2...

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  3. 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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  4. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

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  5. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

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  6. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

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  7. A is an involuntary matrix given by A=|[0, 1,-1], [4,-3, 4], [3,-3, 4]...

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  8. If A is a non-singular matrix such that A A^T=A^T A and B=A^(-1)A^T ,...

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  9. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

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  10. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  11. If A=[[i,-i],[-i ,i]] and B=[[1,-1],[-1 ,1]], t hen ,A^8 equals a.4B b...

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  14. Identify the incorrect statement in respect of two square matrices Aa ...

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  17. Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the fo...

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  18. Let A=[(0,alpha),(0,0)] and (A+I)^(50)=50 A=[(a,b),(c,d)] Then the val...

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  19. If e^(A) is defined as e^(A)=I+A+A^(2)/(2!)+A^(3)/(3!)+...=1/2 [(f(x),...

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  20. Prove that matrix [((b^(2)-a^(2))/(a^(2)+b^(2)),(-2ab)/(a^(2)+b^(2))),...

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