Home
Class 12
MATHS
If A=[0 1 0 0] , prove that (a I+b A)^n=...

If `A=[0 1 0 0]` , prove that `(a I+b A)^n=a^n\ I+n a^(n-1)\ b A` where `I` is a unit matrix of order 2 and `n` is a positive integer.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 1|35 Videos

  • MATRICES

    MOTION|Exercise Exercise - 2(Level-I) (Single correct Option - type Questions)|7 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

If A=[0100], prove that (aI+bA)^(n)=a^(n)I+na^(n-1)bA where I is a unit matrix of order 2 and n is a positive integer.

Let A=[[0,10,0]] show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA where I is the identity matrix of order 2 and n in N

If I is unit matrix of order n, then 3I will be

((1+i)/(1-i))^(4n+1) where n is a positive integer.

If I_(n) is the identity matrix of order n then (I_(n))^(-1)=

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

Minimum value of n for which (2i)^n/(1-i)^(n-2) is positive integer

If A is a non zero square matrix of order n with det(I+A)!=0 and A^(3)=0, where I,O are unit and null matrices of order n xx n respectively then (I+A)^(-1)=

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

Find the least positive integer n such that ((2i)/(1+i))^(n) is a positive integer.

MOTION-MATRICES -Exercise - 4 (Level-II)
  1. If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I ...

    Text Solution

    |

  2. Let A=[1 0 0 0 1 1 0-2 4],I=[1 0 0 0 1 0 0 0 1]a n dA^(-1)=[1/6(A^2+c ...

    Text Solution

    |

  3. If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] and A=[[1,1] , [0,1]] and Q=PAP^...

    Text Solution

    |

  4. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  5. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

    Text Solution

    |

  6. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  7. Match the following {:("(A) The minimum value of "(x^(2)+2x+4)/(x+2)...

    Text Solution

    |

  8. Let A be the set of all 3 xx 3 symmetric matrices all of whose entrie...

    Text Solution

    |

  9. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  10. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  11. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  12. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  13. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  14. Let p be an odd prime number and Tp be the following set of 2 x 2 ma...

    Text Solution

    |

  15. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

    Text Solution

    |

  16. Let M be a 3xx3 matrix satisfying M[{:(0),(1),(0):}]=[{:(-1),(2),(3):}...

    Text Solution

    |

  17. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

    Text Solution

    |

  18. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  19. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

    Text Solution

    |

  20. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  21. Let Ma n dN be two 3xx3 matrices such that M N=N Mdot Further, if M!=N...

    Text Solution

    |