Home
Class 12
MATHS
Prove that: {:|(x,y,z),(x^2,y^2,z^2),(...

Prove that:
`{:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)`

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

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x)

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

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

Without expanding, prove the following |(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=xyz(x-y)(y-z)(z-x)

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

Using properties of determinants, prove that : {:|((x+y)^2,zx,zy),(zx,(z+y)^2,xy),(zy,xy,(z+x)^2)|=2xyz(x+y+z)^3

If x,y,z are different and Delta= {:|(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0 , show that xyz=-1

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b...

    Text Solution

    |

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

    Text Solution

    |

  3. 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

    |

  4. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Prove that |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}| = 4 abc

    Text Solution

    |

  9. Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

    Text Solution

    |

  10. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

    Text Solution

    |

  11. Prove that : |[x+y+z,-z,-y],[-z, x+y+z, -x],[-y,-x,x+y+z]|= 2(x+y)(y+z...

    Text Solution

    |

  12. Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

    Text Solution

    |

  13. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

    Text Solution

    |

  14. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

    Text Solution

    |

  15. Solve for x":"|(a+x,a-x,a-x),(a-x,a+x,a-x),(a-x,a-x,a+x)|=0

    Text Solution

    |

  16. Solve the equation |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64)...

    Text Solution

    |

  17. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

    Text Solution

    |

  18. Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^...

    Text Solution

    |

  19. Prove that |((b+c)^2,ab,ca),(ab,(a+c)^2,bc),(ac,bc,(a+b)^2)|=2abc(a+b...

    Text Solution

    |

  20. If a, b, c are positive and unequal, show that value of the determinan...

    Text Solution

    |