Home
Class 12
MATHS
Prove that the value of each the followi...

Prove that the value of each the following determinants is zero: `|[logx,logy,logz],[ log2x ,log2y ,log2z ],[log3x, log3y ,log3z]|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Prove that , |[1,log_x^y,log_x^z],[log_y^x,1,log_y^z],[log_z^x,log_z^y,1]|=0

Find x if 2log5+1/2 log9 - log3 = logx

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)15

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)60

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)7.5

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)6750

Find the range of the following function y=log_3(log_(1//2)(x^2+4x+4))

For 0ltaltx , the minimum value of function log_a"" x+log_x a is 2.

Solve the following equation of x :2(log)_x a+(log)_(a x)a+3(log)_(a^2x)a=0,a >0

Write the following expressions as log N and find their values. log 10 + 2 log 3 - log 2

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. The value of the determinant |(1^2, 2^2, 3^2, 4^2) ,(2^2, 3^2 ,4^2,5^2...

    Text Solution

    |

  2. If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f...

    Text Solution

    |

  3. Prove that the value of each the following determinants is zero: |[l...

    Text Solution

    |

  4. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

    Text Solution

    |

  5. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

    Text Solution

    |

  6. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

    Text Solution

    |

  7. Which of the following values of alpha satisfying the equation |(1+alp...

    Text Solution

    |

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

    Text Solution

    |

  9. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

    Text Solution

    |

  10. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

    Text Solution

    |

  11. The value of |y z z xx y p2p3r1 1 1|,w h e r ex ,y ,z are respectively...

    Text Solution

    |

  12. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

    Text Solution

    |

  13. Prove that the value of each the following determinants is zero: |s...

    Text Solution

    |

  14. The number of values of k for which the system of the equations (k+1)x...

    Text Solution

    |

  15. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

    Text Solution

    |

  16. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

    Text Solution

    |

  17. Statement 1: "Delta"= |[m y+n z, m q+n r, m b+n c],[k z-m x, k r-m ...

    Text Solution

    |

  18. Prove that |[1, 1, 1]; [a, b, c]; [ bc+a^2, ac+b^2, ab+c^2]|=2(a-b)(b...

    Text Solution

    |

  19. If =|sin theta cos var phi sin theta sin var phi cos theta cos theta c...

    Text Solution

    |

  20. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

    Text Solution

    |