Home
Class 12
MATHS
If A = [[1,1,1],[1,1,1],[1,1,1]], prove ...

If `A = [[1,1,1],[1,1,1],[1,1,1]]`, prove that `A^n = [[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)]], n in N`

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A=[(1,1,1),(1,1,1),(1,1,1)] , prove that A^(n)=[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))],n inN

Prove that "^(n-1)C_3+ ^(n-1)C_4 > ^nC_3 if n >7.

prove: (2^n+2^(n-1))/(2^(n+1)-2^n)=3/2

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n,n(n+1)/2),(0,1,n),(0,0,1)] for all n in N .

Find the value of (3^n × 3^(2n + 1))/(3^(2n) × 3^(n - 1))

If A = [[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]] then Find A+I

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

Prove that 1+1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1).

Prove that .^(n)C_(0) + (.^(n)C_(1))/(2) + (.^(n)C_(2))/(3) + "……" +(. ^(n)C_(n))/(n+1) = (2^(n+1)-1)/(n+1) .

PSEB-MATRICES-Exercise
  1. Using elementary transformations, find the inverse of each of the matr...

    Text Solution

    |

  2. Using elementary transformations find the inverse of matrix A=[[2,-3],...

    Text Solution

    |

  3. Using elementary transformations, find the inverse of each of the matr...

    Text Solution

    |

  4. Using elementary transformations, find the inverse of each of the matr...

    Text Solution

    |

  5. Using elementary transformations find the inverse of the matrix. [[1,3...

    Text Solution

    |

  6. Matrices A and B will be inverse of each other only if:

    Text Solution

    |

  7. Let A = [[0,1],[0,0]] , show that (aI + bA)^n = a^nI + na^(n-1) bA, w...

    Text Solution

    |

  8. If A = [[1,1,1],[1,1,1],[1,1,1]], prove that A^n = [[3^(n-1),3^(n-1),3...

    Text Solution

    |

  9. If A= ((3,-4),(1,-1)), then prove by Mathematical Induction that : A^n...

    Text Solution

    |

  10. If A and B are symmetric matrices, prove that AB – BA is a skew symmet...

    Text Solution

    |

  11. Show that the matrix BAB) is symmetric or skew symmetric according as ...

    Text Solution

    |

  12. Find the values of x, y, z if the matrix A = [[0,2y,z],[x,y,-z],[x,-y,...

    Text Solution

    |

  13. For what values of x : [[1,2,1]][[1,2,0],[2,0,1],[1,0,2]][[0],[2],[x]]...

    Text Solution

    |

  14. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

    Text Solution

    |

  15. ਜੇਕਰ [[x,-5,-1]][[1,0,2],[0,2,1],[2,0,3]][[x],[4],[1]]=O ਹੈ ਤਾਂ x ਦਾ ਮ...

    Text Solution

    |

  16. ਮੈਟ੍ਰਿਕਸ X ਪਤਾ ਕਰੋ ਜੇਕਰ X[[1,2,3],[4,5,6]] = [[-7,-8,-9],[2,4,6]] ਹੈ।

    Text Solution

    |

  17. f A and B are square matrices of the same order such that AB = BA, the...

    Text Solution

    |

  18. . If A = [[alpha,beta],[gamma,-alpha]] is such that A^2 = I, then:

    Text Solution

    |

  19. If the matrix A is both symmetric and skew symmetric, then :

    Text Solution

    |

  20. If A is square matrix such that A^2 = A,then (I+A)^3-7A is equal to:

    Text Solution

    |