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
`because P^(T) = 2 P +I ` ...(i)
`therefore (P^(T))^(T)=(2P+I)^(T) `
`rArr P = 2 P^(T) + I` ..(ii)
From Eqs. (i) and (ii), we get
`P = 2 (2P+I)+I`
`rArr P = -I`
`therefore PX=-IX=-X`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If matrix A = ( 1 2 3) , write AA', Where A' is the transpose of matrix A.

If A is a square matrix such that A^2 = A , then write the value of 7A-(I+A)^3 , where I is an identity matrix.

If A is square matrix such that A^(2)=A , then write the value of 7A-(I+A)^(3) , where I is an identity matrix .

If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A^(T)=9I , where I is 3xx3 identity matrix, then the ordered pair (a, b) is equal to

If P is any square matrix, then the matrix (P+P^(T)) will be:

If order of matrix A is 2 xx 3 and order of matrix B is 3 xx 5 , then order of matrix B 'A' is :

If order of matrix A is 3 xx 3 and order of matrix B is 3 xx 5 , then order of matrix B 'A ' is :

If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A^T," then " B B^T equals

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  2. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |

  6. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  7. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

    Text Solution

    |

  8. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A...

    Text Solution

    |

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

    Text Solution

    |

  16. If A=[(5a,-b),(3,2)] and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

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

    Text Solution

    |

  18. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

    Text Solution

    |

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

    Text Solution

    |

  20. If A=[(2,-3),(-4,1)], then adj (3A^(2)+12 A) is equal to

    Text Solution

    |