Home
Class 12
MATHS
If matrix A is given by A=[[6,11] , [2,4...

If matrix A is given by `A=[[6,11] , [2,4]]` then determinant of `A^(2005)-6A^(2004)` is

A

`2^(2006)`

B

`(-11)2^(2005)`

C

`-2^(2005).7`

D

`(-9) 2^(2004)`

Text Solution

Verified by Experts

The correct Answer is:
B
`|A^(2005)-6A^(2004)|=|A|^(2004)|A-6I|`
`=2^(2004)|(0,11),(2,-2)|=(-22) 2^(2004)=(-11) (2)^(2005)`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Comprehension)|18 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If X is a non-zero column matrix, such that A X=lambda X where lambda is a scalar and the matrix A is [[4,6,6],[1,3,2],[-1,-5,-2]] then sum of distinct values of lambda is

Find the matrix A if [(1,2),(0,1)]A=[(6,1),(2,1)]

For the given matrix A=[(1, 3, 5, 7), (2, 4, 6, 8), (9, 11, 13, 15)] the order of the matrix A^(T) is

Express the matrix A =[[7,1,5],[-4,0,3],[-2,6,1]] as the sum of a symmetric and a skew-symmetric matrices.

Find minors and cofactors of the elements of the determinant {:[( 2,-3,5),( 6,0,4),( 1,5,-7)]:} and verify that a_11 A_31+ a_12A_32+a_13A_33=0

Find the matrix A which satisfies the matrix relation A [(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)].

Without expanding, evaluate the determinants : |(2,3,4),(5,6,8),(6x,9x,12x)|

In [Fe^(11) (CN)_6]^(4-) the central metal ion is

Find the range of y=sin^3x-6sin^2x+11sinx-6.

CENGAGE-MATRICES-Exercise (Single)
  1. If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. ...

    Text Solution

    |

  2. if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h ...

    Text Solution

    |

  3. If matrix A is given by A=[[6,11] , [2,4]] then determinant of A^(2005...

    Text Solution

    |

  4. If A is a non-diagonal involutory matrix, then

    Text Solution

    |

  5. If A and B are two nonzero square matrices of the same order such that...

    Text Solution

    |

  6. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

    Text Solution

    |

  7. If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to

    Text Solution

    |

  8. If A=[(0,x),(y,0)] and A^(3)+A=O then sum of possible values of xy is

    Text Solution

    |

  9. Which of the following is an orthogonal matrix ?

    Text Solution

    |

  10. Let A and B be two square matrices of the same size such that AB^(T)+B...

    Text Solution

    |

  11. In which of the following type of matrix inverse does not exist always...

    Text Solution

    |

  12. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  13. If A=[(a,b,c),(x,y,x),(p,q,r)], B=[(q,-b,y),(-p,a,-x),(r,-c,z)] and If...

    Text Solution

    |

  14. If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),...

    Text Solution

    |

  15. If A=[(a+ib,c+id),(-c+id,a-ib)] and a^(2)+b^(2)+c^(2)+d^(2)=1, then A^...

    Text Solution

    |

  16. Id [1//25 0x1//25]=[5 0-a5]^(-2) , then the value of x is a//125 b. 2a...

    Text Solution

    |

  17. If A=[(1,2),(2,1)] and f(x)=(1+x)/(1-x), then f(A) is

    Text Solution

    |

  18. There are two possible values of A in the solution of the matrix equat...

    Text Solution

    |

  19. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  20. A=[[1, tan x],[-tan x,1]], show that A^(T)A^(-1)=[[cos 2x,-sin 2x],[si...

    Text Solution

    |