Home
Class 12
MATHS
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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-II:|28 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise PART-IV|6 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

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=[[xyz]]!=[[000]] such that

If A is a 3xx3 matrix such that A^T = 5A + 2I , where A^T is the transpose of A and I is the 3xx3 identity matrix, then there exist a column matrix X=[[x],[y],[z]]!=[[0],[0],[0]] then AX is equal to

For two 3xx3 matrices A and B, let A+B=2B' and 3A+2B=I_(3) where B' is the transpose of B and I_(3) is 3xx3 identity matrix,Then:

Let A be a 3xx3 square matrix such that A(a d j\ A)=2I , where I is the identity matrix. Write the value of |a d j\ A| .

If n=p, then the order of the matrix 7X (D) p xx n

If M is a 3xx3 matrix, where det M = I and M M^(T) = I, where I is an identity matrix, prove that det(M-I) = 0

A matrix of order 3xx3 has determinant 2. What is the value of |A(3I)| , where I is the identity matrix of order 3xx3 .

RESONANCE-MATRICES & DETERMINANT-EXERCISE-3
  1. Let a, b and c be three real number satisfying [a,b,c]|{:(,1,9,7),(,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Let P=[a]"be a "3xx3 matrix and let Q=[b]=2^(i+j)a(i) "for" 1 lei, j l...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Let M be a 2 x 2 symmetric matrix with integer entries . Then , ...

    Text Solution

    |

  9. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,...

    Text Solution

    |

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

    Text Solution

    |

  15. Let a,lambda,mu in R, Consider the system of linear equations ax+2y=la...

    Text Solution

    |

  16. Which of the following is (are) NOT the square of a 3xx3 matrix with r...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Let S be the set of all column matrices [(b(1)), (b(2)), (b(3))] such ...

    Text Solution

    |

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

    Text Solution

    |