Home
Class 12
MATHS
If A=[[4,-1,-4],[ 3, 0,-4],[ 3,-1,-3]] ,...

If `A=[[4,-1,-4],[ 3, 0,-4],[ 3,-1,-3]]` , show that `A^2=I_3dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA ENGLISH|Exercise All Questions|181 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA ENGLISH|Exercise All Questions|325 Videos

Similar Questions

Explore conceptually related problems

(i) if A=[{:(4,-1,-4),(3,0,-4),(3,-1,-3):}], then show that A^(2)=I

If A=[[-4,-3,-3],[ 1, 0 ,1],[ 4 ,4, 3]] , show that a d j\ A=A .

If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

If A=|{:(4,-1,-4),(3,0,-4),(3,-1,-3):}| , then show that A=A^(-1)

If A= [[2,4,-1],[-1,0,2]], B=[[3,4],[-1,2],[2,1]] , Show that (AB)'=B'A' .

Find the inverse of A=[[1, 3, 3],[ 1, 4, 3],[ 1, 3, 4]] and verify that A^(-1)A=I_3dot

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

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

If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]] ,then verify that A a d j A = |A|I . Also find A^(-1) .

If A=[3-3 4 2-3 4 0-1 1] , show that A^(-1)=A^3 .

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If omega is a complex cube root of unity, show that ([[1,omega,omega...

    Text Solution

    |

  2. If A=[[1,-2,3],[0, 2 ,-1],[ -4,5-,2]] , find A (adj A) .

    Text Solution

    |

  3. If A=[[4,-1,-4],[ 3, 0,-4],[ 3,-1,-3]] , show that A^2=I3dot

    Text Solution

    |

  4. If [1\ \ 1\ \ x][[1, 0, 2],[ 0 ,2, 1],[ 2, 1, 0]][[1],[ 1],[ 1]]=0 , f...

    Text Solution

    |

  5. If [2 3 5 7][1-3-2 4]=[-4 6-9x] , find xdot

    Text Solution

    |

  6. If [x\ \ 4\ \ 1][[2, 1 ,2],[ 1, 0 ,2],[ 0 ,2,-4]][[x],[4],[-1]]=0 , fi...

    Text Solution

    |

  7. If [1\ -1\ \ x][[0, 1,-1 ],[2 ,1 ,3],[ 1, 1, 1]][[0 ],[1],[ 1]]=0 , fi...

    Text Solution

    |

  8. If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0,1)] , then prove that A^2-A+2...

    Text Solution

    |

  9. If A=[[3 ,1],[-1 ,2]] and I=[[1, 0],[ 0, 1]] , then find lambda so tha...

    Text Solution

    |

  10. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I^2=O .

    Text Solution

    |

  11. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I^2=O .

    Text Solution

    |

  12. Show that the matrix A=[(2, 3), (1, 2)] satisfies the equation A^3-4A...

    Text Solution

    |

  13. Show that the matrix A=[(5, 3), (12 ,7)] then show A^2-12 A-I=O .

    Text Solution

    |

  14. If A=[(3,-5),(-4, 2)] , find A^2-5A-14 Idot

    Text Solution

    |

  15. If A=[[3, 1],[-1 ,2]] , show that A^2-5A+7I=O . Use this to find A^4

    Text Solution

    |

  16. If A=[(3,-2) ,(4,-2)] , find k such that A^2-k A-2I^2=O .

    Text Solution

    |

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

    Text Solution

    |

  18. If A=[(1 ,2 ),(2, 1)] and f(x)=x^2-2x-3 , show that f(A)=O .

    Text Solution

    |

  19. Find dy/dx if logy=5x^2

    Text Solution

    |

  20. Find the value of x for which the matrix product [(2, 0, 7),( 0, ...

    Text Solution

    |