Home
Class 11
MATHS
If I = [(1,0),(0,1)] and E = [(0,1),(0,0...

If `I = [(1,0),(0,1)] and E = [(0,1),(0,0)]` then show that `(aI + bE)^(3) = a^(3)I+3a^(2)bE` where I is identify matrix of order 2.

A

`a^(3)I+3a^(2)bE`

B

`a^(3)I-3a^(2)bE`

C

`a^(3)E+3a^(2)bI`

D

`a^(3)E-3a^(2)bI`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -PRACTICE EXERCISE|41 Videos

  • MATRICES

    AAKASH SERIES|Exercise DETERMINANTS- EXERCISE - I|15 Videos

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -EXERCISE - I|47 Videos

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

if A = [(I,0)(0,-i)] then show that A^(2) = -1 (i^(2)=-1) .

If A= {:[( 1,0,1),(0,1,2),(0,0,4)]:} ,then show that |3A| =27|A|

If A=[{:(1,-2,1),(0,1,-1),(3,-1,1):}] then show that A^3-3A^2-A-3I=O , where I is unit matrix of order 3

If A=[(0,-1),(1,0)],B=[(0,i),(i,0)] then

If A=[(i,0),(0,-i)],B=[(0,-1),(1,0)],C=[(0,i),(i,0)] then

If A=[(1,2,3),(3,-2,1),(4,2,1)] , then show that A^(3)-23A-40I=0

AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES - EXERCISE - II
  1. If A=[(2,-2),(2,3)] and A^(2)-5A+kI(2)=0 then k =

    Text Solution

    |

  2. If A=[(a,b),(c,d)],I=[(1,0),(0,1)] then A^(2)-(a+d)A=

    Text Solution

    |

  3. If I = [(1,0),(0,1)] and E = [(0,1),(0,0)] then show that (aI + bE)^(3...

    Text Solution

    |

  4. IF A=[{:(3,-4),(1,-1):}] then show that A^n=[{:(1+2n,-4n),(n,1-2n):}]...

    Text Solution

    |

  5. if n is a positive integer and A=[(a,0,0),(0,b,0),(0,0,c)] then A^(n) ...

    Text Solution

    |

  6. If A=((coshtheta,sinhtheta),(sinhtheta,coshtheta)) and ninN then A^(n)...

    Text Solution

    |

  7. If A=[(1,1,0),(0,1,1),(0,0,1)] and ninN then A^(n)=

    Text Solution

    |

  8. If A^(2)=2A-I then for n!=2,A^(n)=

    Text Solution

    |

  9. If A=[(i,0,0),(0,i,0),(0,0,i)] then for ninN,A^(4n+1)=

    Text Solution

    |

  10. If A=((0,0),(1,1)) then the value of A+A^(2)+A^(3)+ . . . .A^(n)=

    Text Solution

    |

  11. If A=((2,-2,-4),(-1,3,4),(1,-2,k)) is an idempotent matrix then k =

    Text Solution

    |

  12. IF A=[{:(2,4),(-1,k):}] and A^2=0 then find the value of k

    Text Solution

    |

  13. A=[(1+i,2-3i,4),(7+2i,-i,3-2i)] then the conjugate of A is

    Text Solution

    |

  14. If A is a skew-symmetric matrix and n is odd positive integer, then A^...

    Text Solution

    |

  15. If [(1,-tan theta),( tan theta,1)][(1,tan theta),(-tan theta, 1)]^-1=[...

    Text Solution

    |

  16. If [[x,4,-1]][(2,1,0),(1,0,2),(0,2,4)][(x),(4),(-1)]=0 then x=

    Text Solution

    |

  17. If A=[a(ij)] is a skew symmetric matrix of order 'n' then suma(ii)=

    Text Solution

    |

  18. The number of 2xx2 matrices that can be formed by using 1,2,3,4 withou...

    Text Solution

    |

  19. If a matrix has 13 elements, then the possible dimensions (orders) of ...

    Text Solution

    |

  20. Statement - I, The matrix [(1,-3,-4),(-1,3,4),(1,-3,-4)] is a nilpote...

    Text Solution

    |