Home
Class 12
MATHS
Evaluate the following: {:|(1,a,b+c),(...

Evaluate the following:
`{:|(1,a,b+c),(1,b,c+a),(1,c,a+b)|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following: {:|(b+c,a,a),(b,c+a,b),(c,c,a+b)|

Without expanding, prove the following |(1,a,a^3),(1,b,b^3),(1,c,c^3)|=(a-b)(b-c)(c-a)(a+b+c)

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

Without expanding, prove the following |(a^3+1,a^2,a),(b^3+1,b^2,b),(c^3+1,c^2,c)|=-(a-b)(b-c)(c-a)(abc+1)

Evaluate : triangle = |[1,a,bc],[1,b,ca],[1,c,ab]|

Evaluate |(1,a,a^2),(1,b,b^2),(1,c,c^2)|

The value of |[[1,a,b+c],[1,b,c+a],[1,c,a+b]]| is

Without expanding, prove that : |{:(1, bc, a(b+ c) ),(1, ca, b ( c+ a) ),(1, ab , c( a+ b)):}|=0 .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the following: {:|(b+c,a,a),(b,c+a,b),(c,c,a+b)|

    Text Solution

    |

  2. Evaluate |(x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda)|

    Text Solution

    |

  3. Evaluate the following: {:|(1,a,b+c),(1,b,c+a),(1,c,a+b)|

    Text Solution

    |

  4. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

    Text Solution

    |

  5. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

    Text Solution

    |

  6. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  7. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  8. Without expanding, prove the following |(x+4,x,x),(x,x+4,x),(x,x,x+...

    Text Solution

    |

  9. using properties of determinant, prove that abs{:(y+k , y , y ),(y , y...

    Text Solution

    |

  10. Prove that: {:|(x,y,x+y),(y,x+y,x),(x+y,x,y)| = -2(x^3+y^3)

    Text Solution

    |

  11. By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2]...

    Text Solution

    |

  12. Prove that: {:|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,)|=(a+b)+c)(a^2+b^2+...

    Text Solution

    |

  13. Prove that: {:|(1,a,a),(a,1,a),(a,a,1)|= (2a+1),(1-a)^2

    Text Solution

    |

  14. Prove that: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+...

    Text Solution

    |

  15. Prove that: {:|(1,1,1),(a,b,c),(bc,ca,ab)| = (a-b)(b-c)(c-a)

    Text Solution

    |

  16. Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

    Text Solution

    |

  17. Prove that: {:|(bc,a,1),(ca,b,1),(ab,c,1)| = (a-b)(b-c)(a-c)

    Text Solution

    |

  18. Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,c...

    Text Solution

    |

  19. Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b...

    Text Solution

    |

  20. Prove that: {:|(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc -a^3-b^3-c^...

    Text Solution

    |