Home
Class 12
MATHS
If x != y != z and |[[x,x^2,1+x^3],[y,y^...

If `x != y != z` and `|[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0` then using properties of determinants, show that xyz= -1.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • DIFFERENTIAL EQUATIONS

    PSEB|Exercise Exercise|116 Videos

Similar Questions

Explore conceptually related problems

If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0 , then prove that : xyz(xy+yz+zx)=x+y+z

If x, y, z are all distinct and |(x,x^(2),1+x^(3)),(y,y^(2),1+y^(3)),(z,z^(2),1+z^(3))|=0 then value of x y z is :

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

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

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

Use properties of determinants ot evaluate: {:|(x+y,y+z,z+x),(z,x,y),(1,1,1)|

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)

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

PSEB-DETERMINANTS-Exercise
  1. If x != y != z and |[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]]|=0 the...

    Text Solution

    |

  2. Evaluate the determinant : |[2,4],[-5,-1]|

    Text Solution

    |

  3. Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

    Text Solution

    |

  4. Evaluate the determinant : |[x^2-x+1,x+1],[x+1,x+1]|

    Text Solution

    |

  5. If A = [[1,2],[4,2]], then show that |2A| = 4|A|

    Text Solution

    |

  6. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

    Text Solution

    |

  7. Evaluate the determinant : |[3,-1,-2],[0,0,-1],[3,-5,0]|

    Text Solution

    |

  8. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

    Text Solution

    |

  9. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

    Text Solution

    |

  10. Evaluate the determinant : |[2,-1,-2],[0,2,-1],[3,-5,0]|

    Text Solution

    |

  11. If A = [[1,1,-2],[2,1,-3],[5,4,-9]], find |A|

    Text Solution

    |

  12. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

    Text Solution

    |

  13. Find values of x, if : |[2,3],[4,5]| = |[x,3],[2x,5]|

    Text Solution

    |

  14. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  21. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

    Text Solution

    |