Home
Class 12
MATHS
Let the matrices A=[{:( sqrt3,-2),(0,1):...

Let the matrices `A=[{:( sqrt3,-2),(0,1):}]` and P be any orthogonal matrix such that Q = PAP and let `Rne [r_0] _(2-2)=P'Q^(6) P`then

A

`r_(11) =81 `

B

`r_(1l) =81 sqrt3`

C

` r_(11) -4sqrt3`

D

` r_(11)=-sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    FIITJEE|Exercise ASSIGNMENT PROBLEM (OBJECTIVE) (Level-II)|17 Videos
  • MATRICES

    FIITJEE|Exercise COMPREHENSIONS|8 Videos
  • MATRICES

    FIITJEE|Exercise ASSIGNMENT PROBLEM (SUBJECTIVE) (Level-II)|13 Videos
  • MATHEMATICS TIPS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|21 Videos
  • PARABOLA

    FIITJEE|Exercise NUMERICAL BASED|5 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(6,0),(p,q):}] is a scalar matrix then the value of p and q are

Let the matrix A=[(1,2,3),(0, 1,2),(0,0,1)] and BA=A where B represent 3xx3 order matrix. If the total number of 1 in matrix A^(-1) and matrix B are p and q respectively. Then the value of p+q is equal to

Let A=[(1, 2),(3, 4)] and B=[(p,q),(r,s)] are two matrices such that AB = BA and r ne 0 , then the value of (3p-3s)/(5q-4r) is equal to

A square matrix A is said to be orthogonal if A^T A=I If A is a square matrix of order n and k is a scalar, then |kA|=K^n |A| . Also |A^T|=|A| and for any two square matrix A and B of same order \|AB|=|A||B| On the basis of above information answer the following question: If A=[(p,q,r),(q,r,p),(r,p,q)] be an orthogonal matrix and pqr=1, then p^3+q^3+r^3 may be equal to (A) 2 (B) 1 (C) 3 (D) -1

Let A=[("tan"pi/3,"sec" (2pi)/3),(cot (2013 pi/3),cos (2012 pi))] and P be a 2 xx 2 matrix such that P P^(T)=I , where I is an identity matrix of order 2. If Q=PAP^(T) and R=[r_("ij")]_(2xx2)=P^(T) Q^(8) P , then find r_(11) .

Let P be the set of all non - singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then

Assertion (A) : If the matrix P = [(0,2b,-2),(3,1,3),(3a,3,3)] is a symmetric matrix, then a = (-2)/(3) and b = (3)/(2) Reason (R) : If P is a symmetric matric, then p' = - p

Let P=[[1,0,04,1,016,4,1]] and I be the identity matrix of order 3. If Q=[qij] is a matrix, such that P^(50)-Q=I, then (q_(31)+q_(32))/(q_(21)) equals

FIITJEE-MATRICES -ASSIGNMENT PROBLEM (OBJECTIVE) (Level-I)
  1. {:[(7,1,2),(9,2,1)]:}{:[(3),(4),(5)]:}+2{:[(4),(2)]:} is equal to

    Text Solution

    |

  2. For a invertible matrix A if A (adj A) =[(10,0),(0,10)] then |A...

    Text Solution

    |

  3. Let the matrices A=[{:( sqrt3,-2),(0,1):}] and P be any orthogonal mat...

    Text Solution

    |

  4. A, B, C are three non-zero matrices such that ABC = O, which of the fo...

    Text Solution

    |

  5. If A = [{:( 0,0,0),( 1,0,0),(0,1,0):}] ,then

    Text Solution

    |

  6. If A = [{:( 0,0,0),(0,0,0) ,(0,1,0):}] ,then A is

    Text Solution

    |

  7. If A and B are symmetric matrices of the same order then (A) A-B is sk...

    Text Solution

    |

  8. If A any square matrix then

    Text Solution

    |

  9. If A is a square matrix such that A^(3) =I then the value of A^(-1) ...

    Text Solution

    |

  10. Let A be a square matrix. Then which of the following is not a symmetr...

    Text Solution

    |

  11. If P and Q are symmetric matrices and PQ=QP then which of the followin...

    Text Solution

    |

  12. If A is skew symmetric matrix, then I - A is (where I is identity matr...

    Text Solution

    |

  13. If A=[(4,2),(-1,1)] then (A-21) (A-3I)=

    Text Solution

    |

  14. If A =[{:( a,x,y),( x,b,z),( y,z,c) :}] : a,b,c,x,y,z, "in" (1,2,3,4...

    Text Solution

    |

  15. If A=[(a,b,c),(b,c,a),(c,a,b)],abc=1,A^(T)A=l, then find the value of ...

    Text Solution

    |

  16. Let A is a matrix of order 100xx 50 and B is matrix of order 50xx 75...

    Text Solution

    |

  17. Let Mn =[mg] denotes a square matrix of order n with entries as follow...

    Text Solution

    |

  18. Let A be a 2xx 2 matrix with real entries and det (A)= d ne 0 such ...

    Text Solution

    |

  19. If alpha be the set of integral values of c for which the equations c...

    Text Solution

    |

  20. If A and B matrices commute then

    Text Solution

    |