Home
Class 12
MATHS
Let A=[(1,1,1),(0,1,1),(0,0,1)] prove th...

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`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    PRADEEP PUBLICATION|Exercise EXERCISE|335 Videos

  • MODEL PAPER (2)

    PRADEEP PUBLICATION|Exercise EXERCISE|40 Videos

Similar Questions

Explore conceptually related problems

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

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

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 , for all n in N .

If A= ((-1,-4),(1,3)) , then prove by Mathematical Induction that : A^n = ((1-2n,-4n),(n,1+2n)) , where n in N

If A= ((3,-4),(1,-1)) , then prove by Mathematical Induction that : A^n = ((1+2n,-4n),(n,1-2n)) , where n in N

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

Let a_(0)=2,a_1=5 and for n ge 2, a_n=5a_(n-1)-6a_(n-2) . Then prove by induction that a_(n)=2^(n)+3^(n) forall n in Z^+ .

If a_(1)=1,a_(n+1)=(1)/(n+1)a_(n),a ge1 , then prove by induction that a_(n+1)=(1)/((n+1)!)n in N .

if the product of n matrices [(1,1),(0,1)][(1,2),(0,1)][(1,3),(0,1)]…[(1,n),(0,1)] is equal to the matrix [(1,378),(0,1)] the value of n is equal to

PRADEEP PUBLICATION-MODEL PAPER (1)-EXERCISE
  1. Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x

    Text Solution

    |

  2. If A=[(-1,1,-1),(3,-3,3),(5,-5,5)] and B=[(0,54,3),(1,-3,-3),(-1,4,4)]...

    Text Solution

    |

  3. Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n...

    Text Solution

    |

  4. Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):}. Show that f is continu...

    Text Solution

    |

  5. If x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2), find (dy)/(dx) at x=2.

    Text Solution

    |

  6. The total cost C(x) and the total revenue R(x) associated with the pro...

    Text Solution

    |

  7. Find the interval of increase and decrease of the function f(x)=log(1+...

    Text Solution

    |

  8. Evaluate int (e^x)dx/(sqrt(5-4e^x-e^(2x)) , x<0.

    Text Solution

    |

  9. By examining the chest X-ray, the probability that TB is detected when...

    Text Solution

    |

  10. If veca=(1,1,1), vecb=(0,1,-1) are two given vectors then find a vecto...

    Text Solution

    |

  11. Find the distance of the point (-1, -5, -10) from the point of interse...

    Text Solution

    |

  12. Mathematics teacher of class XII in a school faced an awkward situatio...

    Text Solution

    |

  13. Mathematics teacher of class XII in a school faced an awkward situatio...

    Text Solution

    |

  14. Evaluate: underset(0)overset(pi//2)int(x)/(sinx+cosx)dx

    Text Solution

    |

  15. Evaluate int (sinx)/(sin4x)dx.

    Text Solution

    |

  16. Maximize Z=6x+3y subject to constraints xge0, yge0, 4x+yge80, x+5yge11...

    Text Solution

    |

  17. Find the shortest distance between the lines.(x-8)/3.(y+9)/-16 = (z-10...

    Text Solution

    |

  18. A window has the shape of a rectangle surmounted by an equilateral tri...

    Text Solution

    |

  19. The area lying above x-axis and included between the circle x^2+y^2=8x...

    Text Solution

    |

  20. Solve the following equations by matrix inverse method. 2/x-3/y+3/z=10...

    Text Solution

    |