Home
Class 12
MATHS
Let omega!=1 be cube root of unity and S...

Let `omega!=1` be cube root of unity and `S` be the set of all non-singular matrices of the form `[1a bomega1comega^2theta1],w h e r e` each of `a ,b ,a n dc` is either `omegaoromega^2dot` Then the number of distinct matrices in the set `S` is a. 2 b. `6` c. `4` d. `8`

A

2

B

6

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • MATRICES

    MOTION|Exercise Exercise - 3(Matrix Match - type Questions)|1 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

Let omega!=1 be cube root of unity and S be the set of all non-singular matrices of the form [[1,a,bomega,1,comega^(2),theta,1]], where each of a,b, and c is either omega or omega^(2). Then the number of distinct matrices in the set S is (a) 2 (b) 6 (c) 4 (d) 8

With 1,omega,omega^(2) as cube roots of unity, inverse of which of the following matrices exists?

Let A be the set of all 3xx3 skew-symmetri matrices whose entries are either -1,0, or 1 If there are exactly three os three 1s, and there (-1)'s, then the number of such matrices is

If omega(!=1) is a cube root of unity,then the sum of the series S=1+2 omega+3 omega^(2)+....+3n omega^(3n-1) is

If omega is a cube root of unity,then find the value of the following: (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(8))

If omega is a cube root of unity but not equal to 1, then minimum value of abs(a+bomega+comega^(2)) , (where a,b and c are integers but not all equal ), is

MOTION-MATRICES -Exercise - 4 (Level-I)
  1. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

    Text Solution

    |

  2. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] , then which one of the fo...

    Text Solution

    |

  3. If A and B are square matrices of order n xx n such that A^2-B^2=(A-B)...

    Text Solution

    |

  4. Let {:A=[(1,2),(3,4)]and BA=[(a,0),(0,b)]:},a,b in N Then,

    Text Solution

    |

  5. Let A=[5 5alphaalpha0alpha5alpha0 0 5]dot"I f"|A^2|=25 , then |alpha| ...

    Text Solution

    |

  6. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

    Text Solution

    |

  7. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

    Text Solution

    |

  8. The number of 3 3 non-singular matrices, with four entries as 1 and ...

    Text Solution

    |

  9. Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , whe...

    Text Solution

    |

  10. If omega !=1 is the complex cube root of unity and matrix H=[(omega,...

    Text Solution

    |

  11. Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

    Text Solution

    |

  15. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix ...

    Text Solution

    |

  16. If A is a 3 xx 3 non-singular matrix such that A A^(T) = A^(T)A " and ...

    Text Solution

    |

  17. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  18. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

  19. If A=|{:(,2,-3),(,-4,1):}| then adj (3A^(2)+12A) is equal to

    Text Solution

    |