Home
Class 12
MATHS
The determinant |(b(1)+c(1),c(1)+a(1),...

The determinant
`|(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2)),(b_(3)+c_(3),c_(3)+a_(3),a_(3)+b_(3))|`

A

`[{:(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)),(,a_(3),b_(3),c_(3)):}]`

B

`2[{:(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)),(,a_(3),b_(3),c_(3)):}]`

C

`3[{:(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)),(,a_(3),b_(3),c_(3)):}]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise SECTION-C|11 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise SECTION-D|17 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise EXERCISE-1|7 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

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let /_\=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is

Show that if x_(1),x_(2),x_(3) ne 0 |{:(x_(1) +a_(1)b_(1),,a_(1)b_(2),,a_(1)b_(3)),(a_(2)b_(1),,x_(2)+a_(2)b_(2),,a_(2)b_(3)),(a_(3)b_(1),,a_(3)b_(2),,x_(3)+a_(3)b_(3)):}| =x_(1)x_(2)x_(3) (1+(a_(1)b_(1))/(x_(1))+(a_(2)b_(2))/(x_(2))+(a_(3)b_(3))/(x_(3)))

The value of the determinant Delta = |(1 + a_(1) b_(1),1 + a_(1) b_(2),1 + a_(1) b_(3)),(1 + a_(2) b_(1),1 + a_(2) b_(2),1 + a_(2) b_(3)),(1 + a_(3) b_(1) ,1 + a_(3) b_(2),1 + a_(3) b_(3))| , is

suppose D= |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}| and Dprime= |{:(a_(1)+pb_(1),,b_(1)+qc_(1),,c_(1)+ra_(1)),(a_(2)+pb_(2),,b_(2)+qc_(2),,c_(2)+ra_(2)),(a_(3)+pb_(3),,b_(3)+qc_(3),,c_(3)+ra_(3)):}| . Then

Delta_(1)=det[[a_(1)+pb_(1),b_(1)+qc_(1),c_(1)+ra_(1)a_(2)+pb_(2),b_(1)+qc_(2),c_(2)+ra_(2)a_(3)+pb_(3),b_(3)+qc_(3),c_(3)+ra_(3)]]

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

Let = |(2a_(1)b_(1),a_(1)b_(2)+a_(2)b_(1),a_(1)b_(3)+a_(3)b_(1)),(a_(1)b_(2)+a_(2)b_(1),2a_(2)b_(2),a_(2)b_(3)+a_(3)b_(2)),(a_(1)b_(3)+a_(3)b_(1),a_(3)b_(2)+a_(2)b_(3),2a_(3)b_(3))| Express the determinant D as a product of two determinants. Hence or otherwise show that D = 0.

RESONANCE-MATRICES & DETERMINANT-SECTION-B
  1. If minor of three-one element (i.e.M(31)) in the determinant [{:(,0,1,...

    Text Solution

    |

  2. Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36...

    Text Solution

    |

  3. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b-...

    Text Solution

    |

  4. If a,b,c are positive and ar the p^(th),q^(th),r^(th) terms respective...

    Text Solution

    |

  5. Find the non-zero roots of the equation. (i) Delta=|{:(,a,b,ax+b),(,...

    Text Solution

    |

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

    Text Solution

    |

  7. The value of |(a(1) x(1) + b(1) y(1),a(1) x(2) + b(1) y(2),a(1) x(3) +...

    Text Solution

    |

  8. If [{:(,e^(x),sin x),(,cos x,ln(1+x))]:}=A+Bx+Cx^(2)+....... then find...

    Text Solution

    |

  9. If A and B are squar matrices of order 3 such that |A|=-1, |B|=3 then ...

    Text Solution

    |

  10. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

    Text Solution

    |

  11. |[-1,2,1] , [3+2sqrt2,2+2sqrt2,1] , [3-2sqrt2,2-2sqrt2,1]|=

    Text Solution

    |

  12. If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then th...

    Text Solution

    |

  13. If a, b,c gt 0& x,y,z in R" then the determinant"[{:(,(a^(x)+a^(-x))^(...

    Text Solution

    |

  14. If a,b,c are non-zero real numbers then D=|[b^2 c^2, bc, b+c] , [c^2a^...

    Text Solution

    |

  15. The determinant |(b(1)+c(1),c(1)+a(1),a(1)+b(1)),(b(2)+c(2),c(2)+a(2...

    Text Solution

    |

  16. If x,y,z in R & Delta =|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x+3y,9x...

    Text Solution

    |

  17. The value of the determinant |(cos(theta+phi),-sin(theta+phi),cos2phi)...

    Text Solution

    |

  18. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |