Home
Class 12
MATHS
Let A = [[1,2],[0,1]]. Then A^(n) =...

Let `A = [[1,2],[0,1]]`. Then `A^(n) =`

A

`[[1,2n] ,[0 , -1]]`

B

`[[2,n] ,[0 , 1]]`

C

`[[1,2n] ,[0 , -1]]`

D

`[[1,n] ,[0 , 1]]`

Text Solution

Verified by Experts

The correct Answer is:
A
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

If A= {:[(1,2),(0,1)]:} then A^(n) is

If A=[[1,a],[0,1]], then lim _(n to oo)(1)/(n) A^n is

Let A =[[1,2,2],[2,1,2],[2,2,1]] , then

If A= [[0,1,0],[1,0,0],[0,0,1]] , then A^(2n)= where n is a positive integer.

Let A = [[1,0,0],[1,0,1], [0,1,0]] " satisfies " A^(n) = A^(n-2) + A^(2 ) -I for nge 3 and consider matrix underset(3xx3)(U) with its columns as U_(1), U_(2), U_(3), such that A^(50)U_(1)=[[1],[25],[25]],A^(50) U_(2)=[[0],[1],[0]]and A^(50) U_(3)[[0],[0],[1]] The value of abs(A^(50)) equals

Let X= [[x_1],[x_2],[x_3]], A= [[1,-1,2],[2,0,1],[3,2,1]] and B= [[3],[1],[4]] and if A X=B , then X .

Let, C_(k) = ""^(n)C_(k) " for" 0 le kle n and A_(k) = [[C_(k-1)^(2),0],[0,C_(k)^(2)]] for k ge l and A_(1) + A_(2) + A_(3) +...+ A_(n) = [[k_(1),0],[0, k_(2)]] , then

Let S_(n) = ( 1)/( 1^(3)) + ( 1+2)/( 1^(3) + 2^(3)) +"...." + ( 1+ 2 + "...." + n)/(1^(3) +2^(3)"...."+n^(3)), n = 1,2,3,"....." , Then S_(n) is not greater than :

HIMALAYA PUBLICATION-MATRICES AND DETERMINANTS-QUESTION BANK
  1. Let A = ((1,2),(3,4)) and B = ((a,0),(0,b)), a b in N . Then :

    Text Solution

    |

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

    Text Solution

    |

  3. Let A = [[1,2],[0,1]]. Then A^(n) =

    Text Solution

    |

  4. If [[2+x,3,4],[1,-1,2],[x,1,-5]] is singular matrix then x is

    Text Solution

    |

  5. For the matrix A=[[1,1,0],[1,2,1],[2,1,0]] which is correct?

    Text Solution

    |

  6. If A^(2) - A + I = O , then the inverse of A is :

    Text Solution

    |

  7. If P= [[i,0,-i],[0,-i,i],[-i,i,0]], Q= [[-i,i],[0,0],[i, -i]] then P Q...

    Text Solution

    |

  8. If A= [[2,-1],[-1,2]] and I is the unit matrix of order 2 , then A^2 i...

    Text Solution

    |

  9. Let X= [[x1],[x2],[x3]], A= [[1,-1,2],[2,0,1],[3,2,1]] and B= [[3],[1]...

    Text Solution

    |

  10. Let X= [[x],[y],[z]], D= [[3],[5],[11]], A= [[1,-1,2],[2,1,1],[4,-1,-2...

    Text Solution

    |

  11. If X=[[1,1],[1,1]], then X^n, for n in N is equal to

    Text Solution

    |

  12. Let A and B be two square matrices such that A B=A and B A=B, then A^2...

    Text Solution

    |

  13. If A= [[cos x,sin x,0],[-sin x,cos x,0],[0,0,1]]=f(x) then A^-1=

    Text Solution

    |

  14. A nonsingular matrix A satisfies A^2-A+2 I=0, then A^-1=

    Text Solution

    |

  15. If [[x, y^3],[2,0]]=[[1,8],[2,0]] then [[x,y],[2,0]]^-1=

    Text Solution

    |

  16. If the matrix [[cos theta,sin theta,0],[sin theta,cos theta,0],[0,0,1]...

    Text Solution

    |

  17. If A=[[1,3],[2,1]], then determinant of A^2-2 A is

    Text Solution

    |

  18. If A and B are two matrices such that B=-A^-1 B A then (A+B)^2=

    Text Solution

    |

  19. If A= [[0,2],[3,-4]], k A= [[0,3a],[2b,24]] then the value of k, a, b ...

    Text Solution

    |

  20. If A and B are square matrices of order 3, A is nonsingular and A . B=...

    Text Solution

    |