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 & 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

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

RESONANCE-MATRICES & DETERMINANT-EXERCISE-3
  1. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  2. Let a, b and c be three real number satisfying [a,b,c]|{:(,1,9,7),(,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |