Home
Class 12
MATHS
Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c...

Prove that `|{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)`

Text Solution

Verified by Experts

The correct Answer is:
`abc(1/a+1/b+1/c+1)`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice work|34 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise MISCELLANEOUS EXERCISE - 4|20 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)

Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

If a,b,c and d are the roots of the equation x^(4)+2x^(3)+4x^(2)+8x+16=0 the value of the determinant |{:(1+a,1,1,1),(1,1+b,1,1),(1,1,1+c,1),(1,1,1,1+d):}| is

If the value of the determinant |{:(a,1,1),(1,b,1),(1,1,c):}| is positive then

Let a,b,c be such that b(a+c) ne 0 . If |{:(,a,a+1,a-1),(,-b,b+1,b-1),(,c,c-1,c+1):}|+|{:(,a+1,b+1,c-1),(,a-1,b-1,c+1),(,(-1)^(n+2)a,(-1)^(n+1)b,(-1)^(n)c):}|=0 , Then the value of 'n' is:

Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

If A,B and C are the angle of a non-right angled Delta ABC the value of |{:(tanA,1,1),(1,tanB,1),(1,1,tanC):}| is

Without expanding the determinant prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}|=|{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

If ane0, bne0,cne0 " "and " |{:(1+a,1,1),(1+b,1+2b,1),(1+c,1+c,1+3c):}| =0 the value of |a^(-1)+b^(-1)+c^(-1)| is equal to

KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. Using the property of determinants and without expanding prove the fol...

    Text Solution

    |

  2. Using the properties of determinants, solve the following for x |{:(...

    Text Solution

    |

  3. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

    Text Solution

    |

  4. Using the properties of determinants, prove the following |{:((b+c)^...

    Text Solution

    |

  5. Using the properties of determinants, prove the following |{:((x-2)^...

    Text Solution

    |

  6. Using the properties of determinants, prove the following It 2s=a+b+...

    Text Solution

    |

  7. Using the properties of determinants, prove the following |{:(a^2,b^...

    Text Solution

    |

  8. If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then...

    Text Solution

    |

  9. If a,b,c are A.P then |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}...

    Text Solution

    |

  10. Using the properties of determinants, prove the following |{:(a,b-c,...

    Text Solution

    |

  11. Using the properties of determinants, prove the following |{:((a+b)^...

    Text Solution

    |

  12. Find area of the triangle withh vertices at the point given in each of...

    Text Solution

    |

  13. Find area of the triangle withh vertices at the point given in each of...

    Text Solution

    |

  14. Find area of the triangle withh vertices at the point given in each of...

    Text Solution

    |

  15. Find area of the triangle with vertices at the point given in each of ...

    Text Solution

    |

  16. Find values of k if area of triangle is 4 sq. units and vertices are (...

    Text Solution

    |

  17. Find values of k if the points (3,5), (k,3) and (1,1) are collinear

    Text Solution

    |

  18. Find values of k if area of trianlge is 13 and vertices are (8,2), (k,...

    Text Solution

    |

  19. Find the equation of line passing through the given points using deter...

    Text Solution

    |

  20. Find the equation of line passing through the given points using deter...

    Text Solution

    |