Home
Class 12
MATHS
Show that if x(1),x(2),x(3) ne 0 |{:(x...

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)))`

A

`(a_(1)b_(1))/(x_(1))+(a_(2)b_(2))/(x_(2))+(a_(3)b_(3))/(x_(3))`

B

`-1`

C

`(a_(1)a_(2)a_(3)+b_(1)b_(2)b_(3))/(x_(1)x_(2)x_(3))`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 2 SINGLE CORRECT ANSWER TYPE QUESTIONS)|22 Videos

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (NUMERICAL ANSWER TYPE QUESTIONS)|17 Videos

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

  • DIFFERENTIABILITY AND DIFFERENTIATION

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers |16 Videos

Similar Questions

Explore conceptually related problems

det[[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)]]=

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))|

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

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(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

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

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

the value of the determinant |{:((a_(1)-b_(1))^(2),,(a_(1)-b_(2))^(2),,(a_(1)-b_(3))^(2),,(a_(1)-b_(4))^(2)),((a_(2)-b_(1))^(2),,(a_(2)-b_(2))^(2) ,,(a_(2)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(3)-b_(1))^(2),,(a_(3)-b_(2))^(2),,(a_(3)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(4)-b_(1))^(2),,(a_(4)-b_(2))^(2),,(a_(4)-b_(3))^(2),,(a_(4)-b_(4))^(2)):}| is

MCGROW HILL PUBLICATION-DETERMINANTS-SOLVED EXAMPLES (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
  1. Suppose a,b,c are sides of a scalene triangle. Let Delta=|(a,b,c),(b...

    Text Solution

    |

  2. If A,B and C are angle of a triangle of a triangle ,the value of |{:(...

    Text Solution

    |

  3. Show that if x(1),x(2),x(3) ne 0 |{:(x(1) +a(1)b(1),,a(1)b(2),,a(1)b...

    Text Solution

    |

  4. Let plamda^(4)+qlamda^(3)+rlamda^(2)+slamda+t =|(lamda^(2)+3lamda,la...

    Text Solution

    |

  5. Let Delta=|(1,-4,20),(1,-2,5),(1,2,5x^(2))| Solution set of Delta=0 is

    Text Solution

    |

  6. Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=...

    Text Solution

    |

  7. Suppose a,b,c,gt0 and a,b,c are the pth, qth, rth terms of a G.P. Let ...

    Text Solution

    |

  8. Let omega = - (1)/(2) + i (sqrt3)/(2), then the value of the determina...

    Text Solution

    |

  9. If a,b,c be respectively the p^(th),q^(th)andr^(th) terms of a H.P., ...

    Text Solution

    |

  10. If 1,omega , omega^2 are the cube roots of unity , then Delta=|(1,ome...

    Text Solution

    |

  11. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

    Text Solution

    |

  12. If x=-2 and Delta=|(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)| then numeri...

    Text Solution

    |

  13. If a=omega!=1, is a cube root of unity b=785,c=2008i and Delta=|(a,a...

    Text Solution

    |

  14. for x,x,z gt 0 Prove that |{:(1,,log(x)y,,log(x)z),(log(y)x,,1,,log(y)...

    Text Solution

    |

  15. Let omega!=1 be a cube root of unit and Delta=|(1-omega-omega^(2),2,...

    Text Solution

    |

  16. Suppose x=-1/3(1+sqrt(7)i) and y="cos"(pi)/4+I"sin"(pi)/4 Let Delta=...

    Text Solution

    |

  17. Let x="cos"(pi)/3+i "sin"(pi)/3 and Delta=|(1,x,x^(2)),(x^(2),1,x),(...

    Text Solution

    |

  18. Let f(x)=[2^(-x^(2))[2x^(2)]],x epsilon R ( [ ] denotes the greatest i...

    Text Solution

    |

  19. If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1)...

    Text Solution

    |

  20. Let f:NtoN be defined by f(x)=(x+1)^(2)+x-[sqrt((x+1)^(2)+(x+1))]^(2...

    Text Solution

    |