Home
Class 12
MATHS
The determinant: |(xp+y,x,y),(yp+z,y,z...

The determinant:
`|(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0` if :

A

x, y, z are in A.P

B

x, y, z are in G.P

C

x, y, z are in H.P

D

x y, y z, 2 x are in A.P

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

  • MAXIMA AND MINIMA

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|167 Videos

Similar Questions

Explore conceptually related problems

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

|(x, 4, y+z),(y, 4, z+x),(z, 4, x+y)|=

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

|(x,a,x+a),(y,b,y+b),(z,c,z+c)| = 0

If x,y,z are nonzero real number , then the inverse of matrix A= {:[( x,0,0),( 0,y,0) ,( 0,0,z) ]:} is

Prove that |(x,x^2,yz),(y,y^2,zx),(z,z^2,xy)|= (x-y)(y-z)(z-x)(xy + yz + zx) .

If x,y,z, are in A.P., then value of the det A. where A=[(4,5,6,x),(5,6,7,y),(6,7,8,z),(x,y,z,0)] 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 then show that 1 + xyz = 0

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

Find the values of x, y, z if the matrix A=[(0, 2y,z),(x,y,-z),(x,-y,z)] satisfy the equation A'A=I .

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. Delta=|[log x ,log y, log z],[log 2 x, log 2 y, log 2 z],[log 3 x, log...

    Text Solution

    |

  2. The value of the determine : Delta=|(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)| ...

    Text Solution

    |

  3. The determinant: |(xp+y,x,y),(yp+z,y,z),(0,xp+y,yp+z)|=0 if :

    Text Solution

    |

  4. If f(x)=[[x-3 , 2 x^2-18 , 3 x^3-81],[ x-5 , 2 x^2-50 , 4 x^3-500],[ 1...

    Text Solution

    |

  5. The value of n for which the determinant |[8 C3 , 9 C5 , 10 C7 ],[8 C4...

    Text Solution

    |

  6. [[ 1 , 1 , 1],[ 4 , 3 , 2],[ 4^2 , 3^2 , 2^2 ]] =

    Text Solution

    |

  7. If Delta= [[0 , x , -y ],[-x , 0 , z],[ y , -z , 0 ]] then

    Text Solution

    |

  8. Let Delta=|(1,sintheta,1),(-sin theta,1,sintheta),(-1,-sintheta,1)| , ...

    Text Solution

    |

  9. If [[ p , q-y , r-z],[ p-x , q , r-z ],[ p-x , q-y , r ]]=0, then (p)/...

    Text Solution

    |

  10. A and B are matrices of order three and |A| =4, |B| =-1 . Then the de...

    Text Solution

    |

  11. If A and P are 3xx3 matrices with integral entries such that P ' AP = ...

    Text Solution

    |

  12. Let A be a matrix of order 3 xx 3, and B is its adjoint matrix. If ...

    Text Solution

    |

  13. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

    Text Solution

    |

  14. IF A is a 3 times 3 matrix, |A| ne 0 and |3A|=k|A|, then write the val...

    Text Solution

    |

  15. If alpha , beta and gammaare roots of the equations x^3+px+q=0 then th...

    Text Solution

    |

  16. Delta=|[x+a,b,c],[b,x+c, a],[c,a, x+b]| which of the following is a fa...

    Text Solution

    |

  17. The value of Delta= [[5^2 , 5^3 , 5^4],[ 5^3 , 5^4 , 5^5],[ 5^4 , 5^6 ...

    Text Solution

    |

  18. [[ 0 , p-q , p-r ],[q-p , 0 , q-r],[ r-p , r-q , 0 ]] =

    Text Solution

    |

  19. With the usual notation in the triangle A B C [[ 1 , 1 , 1 ],[ sin A...

    Text Solution

    |

  20. If A= [[-1 , 2 , 4 ],[ 3 , 1 , 0],[ -2 , 4 , 2 ]] and B= [[-2 , 4 ...

    Text Solution

    |