Home
Class 12
MATHS
If A=[[a,b],[0,1]] then prove that A^n=[...

If `A=[[a,b],[0,1]]` then prove that `A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]`

Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    CBSE COMPLEMENTARY MATERIAL|Exercise SIX MARK QUESTIONS|20 Videos

  • MATRICES AND DETERMINANTS

    CBSE COMPLEMENTARY MATERIAL|Exercise TWO MARK QUESTIONS|18 Videos

  • LINEAR PROGRAMMING

    CBSE COMPLEMENTARY MATERIAL|Exercise ONE MARKS QUESTIONS|8 Videos

  • PRACTICE PAPER I

    CBSE COMPLEMENTARY MATERIAL|Exercise Section D|6 Videos

Similar Questions

Explore conceptually related problems

If A=[ab01], prove that A^(n)=[a^(n)b((a^(n)-1)/(a-1))01] for every positive integer n.

If A=[[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all n epsilon N

let A=[[1,01,1]] and I=[[1,00,1]] prove that A^(n)=nA-(n-1)I,n>=1

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n where |a|<1,|b|<1 then prove that sum_(n=0)^oo (ab)^n=(xy)/(x+y-1)

If n. sin(A+2B)=sinA , then prove that: tan(A+B)=(1+n)/(1-n).tanB

If tan(A+B)=ntan(A_B) then prove that (n+1)/(n-1)=(sin2A)/(sin2B)

If A=[{:(1,1),(0,1):}] , prove that A=[{:(1,n),(0,1):}] for all n inN.

If a>b and n is a positive integer,then prove that a^(n)-b^(n)>n(ab)^((n-1)/2)(a-b)

If A=[(1,2),(0,1)], then A^n= (A) [(1,2n),(0,1)] (B) [(2,n),(0,1)] (C) [(1,2n),(0,-1)] (D) [(1,n),(0,1)]

CBSE COMPLEMENTARY MATERIAL-MATRICES AND DETERMINANTS-FOUR MARK QUESTIONS
  1. If A=[(1,-1),(2,1)], B=[(a,1),(b,-1)] and (A+B)^(2)=A^(2)+B^(2)+2AB, t...

    Text Solution

    |

  2. If A=[(0,2b,c),(a,b,-c),(a,-b,c)], then find the value of a, b and c. ...

    Text Solution

    |

  3. If A=[[a,b],[0,1]] then prove that A^n=[[a^n,(b(a^n-1))/(a-1)],[0,1]]

    Text Solution

    |

  4. Find the value of k, if: |(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k...

    Text Solution

    |

  5. If x,y and zinR, and Delta=|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x...

    Text Solution

    |

  6. If |(1,a^2,a^4),(1,b^2,b^4),(1,c^2,c^4)|=k|(1,1,1),(a,b,c),(a^2,b^2,c^...

    Text Solution

    |

  7. Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

    Text Solution

    |

  8. |(1,a^(2)+bc,a^(3)),(1,b^(2)+ac,b^(3)),(1,c^(2)+ab,c^(3))|=-(a-b)(b-c)...

    Text Solution

    |

  9. Using properties of determinants, prove that following: |"a"+"b"+2...

    Text Solution

    |

  10. |[a,b,c],[a-b,b-c,c-a],[b+c,c+a,a+b]|=a^3+b^3+c^3-3abc

    Text Solution

    |

  11. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  12. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

    Text Solution

    |

  13. Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...

    Text Solution

    |

  14. Given A=[(0,-1,2),(2,-2,0)]andB-[(0,1),(1,0),(1,1)]. Find the product ...

    Text Solution

    |

  15. Using properties of determinants, solve the following for x: |x-2 ...

    Text Solution

    |

  16. FInd x when |[x+a, a^2, a^3] , [x+b, b^2, b^3] , [x+c, c^2, c^3]|=0 wh...

    Text Solution

    |

  17. Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and s...

    Text Solution

    |

  18. If x=-4 is a root of a Delta=|(x,2,3),(1,x,1),(3,2,x)|=0, then find th...

    Text Solution

    |

  19. Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...

    Text Solution

    |

  20. prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(...

    Text Solution

    |