Home
Class 12
MATHS
If omega is a non-real cube root of unit...

If `omega` is a non-real cube root of unity, then `Delta = |(a_(1) + b_(1) omega,a_(1) omega^(2) + b_(1),a_(1) + b_(1) + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) omega^(2) + b_(2),a_(2) + b_(2) omega + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) omega^(2) + b_(3),a_(3) + b_(3) omega + c_(3) omega^(2))|` is equal to

A

0

B

`-1`

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    DISHA PUBLICATION|Exercise EXERCISE -1 CONCEPT BUILDER|65 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • DIFFERENTIAL EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

If omega is a complex cube root of unity, then value of Delta=|(a_(1)+b_(1)omega, a_(1)omega^(2)+b_(1),c_(1)+b_(1)omega),(a_(2)+b_(2)omega,a_(2)omega^(2)+b_(2),c_(2)+b_(2)omega),(a_(3)+b_(3)omega,a_(3)omega^(2)+b_(3),c_(3)+b_(3)omega)| is

If omega pm 1 is a cube root of unity, the value of (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = ?

if w is a complex cube root to unity then value of Delta =|{:(a_(1)+b_(1)w,,a_(1)w^(2)+b_(1),,c_(1)+b_(1)bar(w)),(a_(2)+b_(2)w,,a_(2)w^(2)+b_(2),,c_(2)+b_(2)bar(w)),(a_(3)+b_(3)w,,a_(3)w^(2)+b_(3),,c_(3)+b_(3)bar(w)):}| is

If omega (ne 1) is a cube root of unity and (1 + omega^(2))^(11) = a + b omega + c omega^(2) , then (a, b, c) equals

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

DISHA PUBLICATION-DETERMINANTS-EXERCISE -2 CONCEPT APPLICATOR
  1. If m is a positive integer and Dr=|2r-1\ ^m Cr1m^2-1 2^m m+1s in^2(...

    Text Solution

    |

  2. If x,y and z are the integers in AP lying between 1 and 9 and x 51, ...

    Text Solution

    |

  3. If omega is a non-real cube root of unity, then Delta = |(a(1) + b(1) ...

    Text Solution

    |

  4. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

    Text Solution

    |

  5. Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....

    Text Solution

    |

  6. If |{:(x^(n),x^(x+2),x^(2n)),(1,x^(a),a),(x^(n+5),x^(a+6),x^(2n+5)):}|...

    Text Solution

    |

  7. The value of the determinant |{:(1^(2),2^(2),3^(2),4^(2)),(2^(2),3^(2)...

    Text Solution

    |

  8. The value of the determinant |{:(1 ,(5^(2x)-5^(-2x))^(2),(5^(2x)-5^(-2...

    Text Solution

    |

  9. If a^(2)+b^(2)+c^(2)=-2 and |{:(1+a^(2)x,(1+b^(2))x,(1+c^(2))x),((...

    Text Solution

    |

  10. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  11. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  12. If f(x) = |{:(cos^(2)x, cosx.sinx, -sin x),(cos x sinx ,sin^(2)x ,cos ...

    Text Solution

    |

  13. the value of the determinant |{:((a(1)-b(1))^(2),,(a(1)-b(2))^(2),,...

    Text Solution

    |

  14. f'(x) = |{:(cos x , x , 1),(2sin x,x^(2),2x),(tan x, x,1):}| . The val...

    Text Solution

    |

  15. If the matrix A = [{:(y+a,b,c),(a,y+b,c),(a,b,y+c):}] has rank 3, then

    Text Solution

    |

  16. If the system of linear equations x1 + 2x2 + 3x3 = 6, x1 + 3x2 + 5x3 =...

    Text Solution

    |

  17. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

    Text Solution

    |

  18. Let A=[a(ij)](3xx3) be such that a(ij)=[{:(3, " when",hati=hatj),(0,,h...

    Text Solution

    |

  19. Let lambda "and" alpha be real. Let S denote the set of all values of ...

    Text Solution

    |

  20. Prove that the value of each the following determinants is zero: |s...

    Text Solution

    |