Home
Class 12
MATHS
The value of the determinant |{:(1,x,x^2...

The value of the determinant `|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}|` is equal to

A

0

B

xyz

C

`(x-y)(y-z)(z-x)`

D

`xy+yz+zx`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION - B|21 Videos

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION - C|7 Videos

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise Try Yourself|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise section - J|6 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

Similar Questions

Explore conceptually related problems

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Given that xyz = -1 , the value of the determinant |(x,x^(2),1 +x^(3)),(y,y^(2),1 + y^(3)),(z,z^(2),1 +z^(3))| is

The value of the determinant |{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x^(2)),(z^(2),1,x^(2)+y^(2)):}| is :

The value of |{:(x,x^2-yz,1),(y,y^2-zy,1),(z,z^2-xy,1):}| is

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

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

Without expanding evaluate the determinant |(x^2+x^(-1))^2(a^2-a^(-1))^2 1(a^y+a^(-y))^2(a^y-a^(-y))^2 1(a^2+a^(-z))^2(a^z-a^(-z))^2 1|, where a , >0a n dx , y , z in Rdot

Prove that the value of each the following determinants is zero: (a^(x)+a^(-x))^(2),(a^(x)-a^(-x))^(2),1(b^(y)+b^(-y))^(2),(b^(y)-+b^(-y))^(2),1(c^(z)+c^(-z))^(2),(c^(z)-c^(-z))^(2),1]|

AAKASH INSTITUTE-DETERMINANTS -SECTION A
  1. Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| ...

    Text Solution

    |

  2. If A is a square matrix of order n , prove that |Aa d jA|=|A|^n

    Text Solution

    |

  3. The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is eq...

    Text Solution

    |

  4. The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is eq...

    Text Solution

    |

  5. If A is 3xx3 matrix and |A|=4, then |A^(-1)| is equal to

    Text Solution

    |

  6. If A is a square matrix of order 3 such that ||A =3, then find the val...

    Text Solution

    |

  7. If A, B and C are three sqare matrices of the same order such that A ...

    Text Solution

    |

  8. If delta =|(a1,b1,c1),(a2,b2,c2),(a3,b3,c3)| then the value of |(2a1+3...

    Text Solution

    |

  9. If the system of equations x + 4ay + az = 0 and x + 3by + bz = 0 and x...

    Text Solution

    |

  10. Let ax^3+bx^2+cx+d=|{:(3x,x+1,x-1),(x-3,-2x,x+2),(x+3,x-4,5x):}| then ...

    Text Solution

    |

  11. Let x + y + z = 6, 4x + lambday - lambdaz = 0,3x + 2y - 4z = -5. The v...

    Text Solution

    |

  12. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

    Text Solution

    |

  13. The value of theta lying between 0 and pi/2 and satisfying the equatio...

    Text Solution

    |

  14. |[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]|=0

    Text Solution

    |

  15. If |{:(4,-4,0),(a,b+4,c),(a,b,c+4):}|=0, then a+b+c is equal to

    Text Solution

    |

  16. The equation |{:(x-2,3,1),(4x-2,10,4),(2x-1,5,1):}|=0 is satisfied by

    Text Solution

    |

  17. |{:(x,4, y+z),(y,4,z+x),(z,4,x+y):}| is eqaual to

    Text Solution

    |

  18. |{:(a,b,c),(b,c,a),(c,a,b):}| is equal to

    Text Solution

    |

  19. The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

    Text Solution

    |

  20. The value of the determinant |{:(1,logba),(logab,1):}| is equal to

    Text Solution

    |