Home
Class 12
MATHS
Prove the following by principle of math...

Prove the following by principle of mathematical induction If `A=[[3,-4] , [1,-1]]`, then `A^n=[[1+2n, -4n] , [n, 1-2n]]` for every positive integer `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

If A=[[3,-4],[1,-1]] , then prove that A^n=[[1+2n,-4n],[n,1-2n]] , where n is any positive integer.

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: IfA=[[a,1],[ 0,a]],t h e nA^n=[[a^n,n a^(n-1)],[0,a^n]] for every positive integer n.

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: 1/2+1/4+1/8++1/(2^n)=1-1/(2^n)

Prove the following by the principle of mathematical induction: \ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

If a is a non-zero real or complex number. Use the principle of mathematical induction to prove that: If A=[a1 0a] , then A^n=[a^nn a^(n-1)0a^n] for every positive integer ndot

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

Prove the following by the principle of mathematical induction: n^3-7n+3 is divisible 3 for all n in N .

Prove the following by the principle of mathematical induction: \ 1. 3+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. Let f(x)=x^2-5x+6 then find f(A) when A=[[2,0,1] , [2,1,3] , [1, -1, 0...

    Text Solution

    |

  2. If A=[3 1-1 2], show that A^2-5A+7I=0

    Text Solution

    |

  3. Prove the following by principle of mathematical induction If A=[[3,-4...

    Text Solution

    |

  4. If Aalpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove tha...

    Text Solution

    |

  5. If Aalpha=[cosalphasinalpha-sinalphacosalpha] , then prove that (Aalph...

    Text Solution

    |

  6. If a is a non-zero real or complex number. Use the principle of mat...

    Text Solution

    |

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

    Text Solution

    |

  8. Under what conditions is the matrix equation A^2-B^2=(A-B)(A+B) is ...

    Text Solution

    |

  9. If A is any mxxn such that A B and B A are both defined show that B...

    Text Solution

    |

  10. A ,\ B are two matrices such that A B and A+B are both defined; sho...

    Text Solution

    |

  11. If A and B are square matrices of order n , then prove that A and B...

    Text Solution

    |

  12. If A B=A and B A=B , then show that A^2=A , B^2=B .

    Text Solution

    |

  13. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

    Text Solution

    |

  14. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

    Text Solution

    |

  15. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

    Text Solution

    |

  16. Use matrix multiplication to divide Rs. 30,000 in two parts such that ...

    Text Solution

    |

  17. Three schools A ,\ B and C organised a mela for collecting funds fo...

    Text Solution

    |

  18. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

    Text Solution

    |

  19. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

    Text Solution

    |

  20. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

    Text Solution

    |