Home
Class 12
MATHS
Let A=[(-1,-4),(1,3)], prove by Mathemat...

Let `A=[(-1,-4),(1,3)]`, prove by Mathematical Induction that `A^(n)=[(1-2n,-4n),(n,1+2n)]`, where `n in N`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MODERN PUBLICATION|Exercise Exercise 3 (d) Long Answer Type Questions II|2 Videos

  • MATRICES

    MODERN PUBLICATION|Exercise Exercise 3 (e ) Short Answer Type Questions|16 Videos

  • MATRICES

    MODERN PUBLICATION|Exercise Exercise 3 (d ) Short Answer Type Questions|20 Videos

  • LINEAR PROGRAMMING

    MODERN PUBLICATION|Exercise Chapter Test|12 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

Similar Questions

Explore conceptually related problems

Let A=[(-1,-4),(1,3)] , by Mathematical Induction prove that : A^(n)[(1-2n,-4n),(n,1+2n)] , where n in N .

Prove by mathematical induction that sum_(r=0)^(n)r^(n)C_(r)=n.2^(n-1), forall n in N .

Show using mathematical induciton that n!lt ((n+1)/(2))^n . Where n in N and n gt 1 .

If A=[[3,-4] , [1,-1]] then by the method of mathematical induction prove that A^n=[[1+2n,-4n] , [n,1-2n]]

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

Prove by Principle of Mathematical Induction that (10^(2n -1) + 1) is divisible by 11 for all n in N .

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

Using the principle of mathematical induction prove that (1+x)^(n)>=(1+nx) for all n in N, where x>-1

If A,=[[3,-41,1]], then prove that A^(n),=[[1+2n,-4n][2n], where n is any positive integer.

MODERN PUBLICATION-MATRICES-Exercise 3 (d) Long Answer Type Questions I
  1. If A=[3 1-1 2] , show that A^2-5A+7I=O . Use this to find A^4

    Text Solution

    |

  2. Let A ={:[(2,0,1),(2,1,3),(1,-1,0)] and f(x) = x^(2) -5x + 6 , find f(...

    Text Solution

    |

  3. यदि A= [[2,0,1],[2,1,3],[1,-1,0]], तब A^(2) - 3A + 2I का मान ज्ञात क...

    Text Solution

    |

  4. if A=[{:(3,1),(-1,2):}],show that A^(2)-5A+7I=0.

    Text Solution

    |

  5. If M=[(7,5),(2,3)], then verify the equation : M^(2)-10M+11I(2)=O

    Text Solution

    |

  6. If A+l={:[(2,2,3),(3,-1,1),(4,2,2)]:} then show that A^(3)-23A-40l=0

    Text Solution

    |

  7. If A=[1 0 2 0 2 1 2 0 3] , prove that A^3-6A^2+7A+2I=0

    Text Solution

    |

  8. If A=[{:(-1,2),(3,1):}], find f(A), where f(x)=x^(2)-2x+3.

    Text Solution

    |

  9. If A=[(3,1),(-1,2)], then find f (A), where f(x)=x^(2)-5x+7.

    Text Solution

    |

  10. If A=[1 0-1 7] , find k such that A^2-8A+k I=O .

    Text Solution

    |

  11. If A A=[3-2 4-2]and I=[1 0 0 1], find k so that A^2=k A-2I.

    Text Solution

    |

  12. If A=[(0,3),(-7,5)] and I=[(1,0),(0,1)], then find 'k' so that k^(2)=5...

    Text Solution

    |

  13. Solve system of linear equations, using matrix method, x y" "+" "2...

    Text Solution

    |

  14. Let A=[0 1 0 0]show that (a I+b A)^n=a^n I+n a^(n-1)b A, where I is t...

    Text Solution

    |

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

    Text Solution

    |

  16. Let A=[(-1,-4),(1,3)], prove by Mathematical Induction that A^(n)=[(1-...

    Text Solution

    |

  17. If A=[[costheta,-sintheta],[sintheta,costheta]] then show that A^n = [...

    Text Solution

    |

  18. If A=[costhetaisinthetaisinthetacostheta], then prove by principal of ...

    Text Solution

    |

  19. A trust fund has Rs 30,000 that must be invested in two different t...

    Text Solution

    |

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

    Text Solution

    |