Home
Class 11
MATHS
If k gt1, and the determinant of the mat...

If `k gt1`, and the determinant of the matrix `A^(2)`, where `A=[(k,kalpha, alpha),(0,alpha, k alpha),(0,0,k)]` is `k^(2)` then `|alpha|=`

A

`(1)/(k^(2))`

B

k

C

`k^(2)`

D

`1/k`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS-PRACTICE EXERCISE|39 Videos
  • MATRICES

    AAKASH SERIES|Exercise INVERSE OF A MATRIX- EXERCISE - I|21 Videos
  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - I|15 Videos
  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 then |alpha| equals

If A=[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0,0,1)] then (AdjA)^(T)=

If F(alpha)=|(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,0,1)| then det F(alpha)=

If (1+tan alpha)(1+tan 4alpha)=2, alpha epsilon(0,(pi)/(6)) , then alpha= .

If (1 + tan alpha) (1 + tan 4 alpha) = 2, alpha in (0, (pi)/(16)) , then alpha =

If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+alpha^(3)+alpha^(4)+alpha^(5))/(alpha+1)

Find the inverse of each of the matrices (if it exists ) {:[( 1,0,0),( 0 ,cos alpha , sin alpha ),( 0, sin alpha , -cos alpha ) ]:}

If (1+ tan alpha)(1+ tan 4alpha)=2, alpha in (0, pi//16) , then alpha is equal to:

AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II
  1. |(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

    Text Solution

    |

  2. Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...

    Text Solution

    |

  3. If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...

    Text Solution

    |

  4. If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...

    Text Solution

    |

  5. If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|

    Text Solution

    |

  6. |(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

    Text Solution

    |

  7. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

    Text Solution

    |

  8. If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=

    Text Solution

    |

  9. If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...

    Text Solution

    |

  10. Let |{:(x^(2)+x+1,x+1,2x-3),(3x^(2)-1,x+2,x-1),(x^(2)+5x+1,2x+3,x+4):}...

    Text Solution

    |

  11. If |(a,b,a alpha+b),(b,c, b alpha+c),(a alpha+b, b alpha+c,0)|=0 then

    Text Solution

    |

  12. If a,b,c are the p^(th),q^(th),r^(th) terms in H.P. then |{:(bc,p,1),(...

    Text Solution

    |

  13. If |(3x-8,3,3),(3,3x-8,3),(3,3,3x-8)|=0 then x=0

    Text Solution

    |

  14. If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 the...

    Text Solution

    |

  15. If x=-1 is a root of the equation |{:(2-x,3,3),(3,4-x,5),(3,5,4-x):}|=...

    Text Solution

    |

  16. If one of the roots of |(3,5,x),(7,x,7),(x,5,3)|=0 is -10, then the ot...

    Text Solution

    |

  17. If |(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z)|=64 then x=

    Text Solution

    |

  18. If a,b,c, are in A.P. then |(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c)|...

    Text Solution

    |

  19. If a,b,c are pth, qth rth terms respectivelyy of a G.P then |(loga, p,...

    Text Solution

    |

  20. If |{:(0,sinalpha,sinbeta),(sinalpha,0,singamma),(sinbeta,singamma,0):...

    Text Solution

    |