Home
Class 12
MATHS
If A is a square matrix, using mathem...

If `A` is a square matrix, using mathematical induction prove that `(A^T)^n=(A^n)^T` for all `n in N` .

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

Using mathematical induction prove that : d/(dx)(x^n)=n x^(n-1) for all n in NN .

Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all positive integers n.

Using the principle of mathematical induction, prove that n<2^n for all n in N

Using Mathematical induction, prove that 10 ^(n)+3.4^(n+2)+5 is divisible by 9 for all ninN .

Using mathemtical induction prove that 3^(2n + 2)- 8n - 9 is divisible by 64 for all n in N .

Using mathematical induction, to prove that 1*1!+2*2!+3.3!+ . . . .+n*n! =(n+1)!-1 , for all n in N

By using principle of mathematical induction, prove that 2+4+6+….2n=n(n+1), n in N

Using mathematical induction prove that n^(3)-7n+3 is divisible by 3, AA n in N

Using mathematical induction , to prove that 7^(2n)+2^(3n-3). 3^(n-1) is divisible by 25 , for al n in N

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If B ,\ C are n rowed square matrices and if A=B+C , B C=C B , C^2=...

    Text Solution

    |

  2. If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n)...

    Text Solution

    |

  3. If A is a square matrix, using mathematical induction prove that (A...

    Text Solution

    |

  4. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

    Text Solution

    |

  5. Give examples of matrices A and B such that A B!=B A . (ii) A and B...

    Text Solution

    |

  6. Give examples of matrices A and B such that A B=O but B A!=O . (ii)...

    Text Solution

    |

  7. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

    Text Solution

    |

  8. If A and B are square matrices of the same order, explain, why in g...

    Text Solution

    |

  9. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

    Text Solution

    |

  10. If A and B are square matrices of the same order such that A B=B A ...

    Text Solution

    |

  11. Let A=[[1 ,1, 1],[ 3, 3, 3]] , B=[[3,1], [5, 2],[-2, 4]] and C=[[4,2],...

    Text Solution

    |

  12. Three shopkeepers A ,\ B\ a n d\ C go to a store to buy stationary....

    Text Solution

    |

  13. The cooperative stores of a particular school has 10 dozen physics ...

    Text Solution

    |

  14. In a legislative assembly election, a political group hired a public...

    Text Solution

    |

  15. A trust fund has Rs. 30000 that must be invested in two different ty...

    Text Solution

    |

  16. To promote making of toilets for women, an organisation tried to ge...

    Text Solution

    |

  17. There are two families A and B.In family A, there are 4 men, 6 women a...

    Text Solution

    |

  18. In a parliament election, a political party hired a public relations...

    Text Solution

    |

  19. The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and ...

    Text Solution

    |

  20. A trust invested some money in two types of bonds. The first bond pays...

    Text Solution

    |