Home
Class 12
MATHS
IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,...

IF `a+b+c ne 0` and `{:|(a,b,c),(b,c,a),(c,a,b)|`=0, then using properties of determinants, prove that `a=b=c`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTION -II)|3 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC-2 SOLUTIONS OF SYSTEM OF LINEAR EQUATIONS (LONG ANSWER TYPE QUESTIONS -II )|24 Videos

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (SHORT ANSWER TYPE QUESTIONS-II)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos

  • DIFFERENTIAL EQUATIONS

    OSWAAL PUBLICATION|Exercise HOMOGENEOUS DIFFERENTIAL EQUATIONS (Long Answer Type Questions - III)|8 Videos

Similar Questions

Explore conceptually related problems

If a ne 6, b , c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 , then abc =

|(0,a,-b),(-a,0,-c),(b,c,0)| = 0

|(a - b, b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c)|=0

If a+b+c=0 , one root of : |(a-x,c,d),(c,b-x,a),(b,a,c-x)|=0 is :

Prove that |(b+c,a,a),(b,c+a,b),(c,c,a+b)|= 4ac

If a, b, c are in HP., then a/(b+c),b/(c+a),c/(a+b) are in

|(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b))|= 0

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...

    Text Solution

    |

  2. Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...

    Text Solution

    |

  3. IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...

    Text Solution

    |

  4. Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Find the equation of the line joining A( 1,3) and B (0,0) using det...

    Text Solution

    |

  8. Using properties of determinants, prove the following: |xx+y x+2y\...

    Text Solution

    |

  9. Using properties of determinants, prove the following: |alphabetag...

    Text Solution

    |

  10. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

    Text Solution

    |

  11. [[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3

    Text Solution

    |

  12. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

    Text Solution

    |

  13. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

    Text Solution

    |

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

    Text Solution

    |

  15. Using the Properties of determinants, prove that following: {:|(-a^2...

    Text Solution

    |

  16. Using the Properties of determinants, prove the following: {:|(1,1...

    Text Solution

    |

  17. If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...

    Text Solution

    |

  18. Using properties of determinants, solve the following for x: |x-2 ...

    Text Solution

    |

  19. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

    Text Solution

    |

  20. Using Properties of determinants, solve the following for x: {:|(x+a...

    Text Solution

    |