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

If P is a `3xx3` matrix such that `P^(T) = 2 P + 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]]ne[[0],[0],[0]]` such that

A

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

B

PX=X

C

PX=2X

D

PX=-X

Text Solution

Verified by Experts

The correct Answer is:
B
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Consider the set A of all matrices of order 3 xx 3 with entries 0 or 1...

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  2. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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

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  4. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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

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

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  7. Given , 2x-y+2z=2, x-2y+z=-4, x+y+lambdaz=4, then the value of lam...

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  8. The number of values of k for which the system of the equations (k+1)x...

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  9. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  10. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  11. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

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

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  13. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  14. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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

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  16. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  17. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  18. If the adjoint of a 3 xx 3 matrix P is [{:(,1,4,4),(,2,1,7),(,1,1,3):}...

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  19. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

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  20. Which of the following values of alpha satisfying the equation |(1+alp...

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