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If P is a 3xx3 matrix such that P^T = 2P...

If P is a `3xx3` matrix such that `P^T = 2P+I`, where `P^T` is the transpose of P and I is the `3xx3` identity matrix, then there exists a column matrix, `X = [[x],[y],[z]]!=[[0],[0],[0]]` such that

A

`PX=[(0),(0),(0)]`

B

PX = X

C

PX = 2X

D

PX = X

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The correct Answer is:
D
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MOTION-MATRICES -Exercise - 4 (Level-II)
  1. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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

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  3. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  4. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  5. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

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  6. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

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  7. Let M be a 3xx3 matrix satisfying M[{:(0),(1),(0):}]=[{:(-1),(2),(3):}...

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  8. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

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  9. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

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  10. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

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  11. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

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  12. Let Ma n dN be two 3xx3 matrices such that M N=N Mdot Further, if M!=N...

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  13. Let M be a 2 × 2 symmetric matrix with integer entries. Them M is inve...

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  14. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

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  15. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

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  16. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

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  17. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

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  18. Which of the following is (are) NOT the square of a 3 xx 3 matrix with...

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  19. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

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  20. Let P be a matrix of order 3xx3 such that all the entries in P a...

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