Home
Class 12
MATHS
If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z...

If `[[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0`
then prove that xyz=1 when x,y,z are non zero and unequal.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MBD PUBLICATION|Exercise QUESTION TYPE|4 Videos

  • DIFFERENTIAL EQUATIONS

    MBD PUBLICATION|Exercise QUESTION BANK|87 Videos

Similar Questions

Explore conceptually related problems

If [[x+y,x-2],[2x-z,0]]=[[2,5],[3,1]] then the values of x,y,z.

If [[x+y,x-z],[2x-y,0]]=[[2,2],[1,0]] find the values of x,y,z.

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

cos^(-1)x+cos^(-1)y+cos^(-1)z=pi ,then prove that, x^2+y^2+z^2+xyz=1

If A=[[1,-2,1],[0,-1,1],[2,0,-3]] then find A^(-1) and hence solve the system of equations x-2y + z = 0 , -y + z = -2 and 2x-3z= 10.

If [{:(x+y,x-z),(2x-y,0):}]=[{:(2,2),(1,0):}] ,find the value of x,y,z.

If cos^-1x+cos^-1y+cos^-1z=pi , prove that x^2+y^2+z^2+2xyz=1 .

If [{:(x-y,2x+z),(2x-y,3z+w):}]=[{:(-1,5),(0,13):}] then find x,y,z and w .

MBD PUBLICATION-DETERMINATES-QUESTION BANK
  1. For what value of lamda the system of equations x+y+z=6, 4x+lamda y-...

    Text Solution

    |

  2. If A is a 3xx3 matrix and absA=2, then which matrix is represented by ...

    Text Solution

    |

  3. If A=[[0,-tan(alpha/2)],[tan(alpha/2),0]] show that (I+A) =(I-A)[[c...

    Text Solution

    |

  4. Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+...

    Text Solution

    |

  5. Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a...

    Text Solution

    |

  6. Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

    Text Solution

    |

  7. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

    Text Solution

    |

  8. Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^...

    Text Solution

    |

  9. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

    Text Solution

    |

  10. Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] =a^3+b^...

    Text Solution

    |

  11. Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =...

    Text Solution

    |

  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

    Text Solution

    |

  13. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

    Text Solution

    |

  14. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

    Text Solution

    |

  15. Without expanding show that the following determinant is equal to Ax+B...

    Text Solution

    |

  16. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

    Text Solution

    |

  17. If a1, a2,........,an are in G.P. and ai gt 0 for every i, then find t...

    Text Solution

    |

  18. If f(x)=[[1+sin^2x,cos^2x,4sin2x],[sin^2x,1+cos^2x,4sin2x],[sin^2x,cos...

    Text Solution

    |

  19. If fr(x),gr(x),hr(x),r=1, 2, 3 are polynomials in x such that fr(a)=...

    Text Solution

    |

  20. If f(x)=[[cosx,sinx,cosx],[cos2x,sin2x,2cos2x],[cos3x,sin3x,3cos3x]] ...

    Text Solution

    |