Home
Class 12
MATHS
using properties of determinant, prove t...

using properties of determinant, prove that `abs{:(y+k , y , y ),(y , y + k , y ),(y, y , y+k):}= k^(2) ( 3y + k)`

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

Using the properties of determinats, show that |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^(2)(3y+k)

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+z+2x,y],[z,z,z+x+2y]| = 2(x+y+z)^3

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

Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. 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

    |

  15. Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b...

    Text Solution

    |

  16. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

    Text Solution

    |

  17. Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,...

    Text Solution

    |

  18. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

    Text Solution

    |

  19. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

    Text Solution

    |

  20. Without expanding, prove the following |(b+c,c+a,a+b),(c+a,a+b,b+c)...

    Text Solution

    |