Home
Class 12
MATHS
If A=[ (3,-2),( 4 ,-2) ] and I=[(1,0),(0...

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

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

If A A=[[3,-2],[ 4,-2]] and I=[[1, 0],[ 0, 1]] , find k so that A^2=k A-2I .

If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O .

If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

If A = [ (-3 , 2) , (1, -1)] and I = [(1,0) , (0, 1)] , find the scalar k so that A^2 +I = kA .

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

(i) if A=[{:(1,-4),(3,1):}]and b=[{:(1,0,5),(-2,4,3):}], then show that : (AB)'=B'A' (ii) if A=[{:(2,3),(0,1):}]and B=[{:(3,4),(2,1):}], then prove that : (AB)'=B'A'

If A=[{:(,3,1),(,-1,2):}] and I=[{:(,1,0),(,0,1):}] ,find A^2-5A+7I .

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify that (i) (A')'=A (ii) (AB)'=B'A'

If A=[{:(4,1),(3,2):}] and I=[{:(1,0),(0,1):}] then A^(2)-6A is equal to : a) 3I b) -5I c) 5I d) none of these

if A'=[{:(3,4),(-1,2),(0,1):}]and B=[{:(-1,2,1),(1,2,3):}], then verify that (i) (A+B)'=A'+B'(ii) (A-B)'=A'-B'

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If [x\ \ 4\ \ 1][[2, 1 ,2],[ 1, 0 ,2],[ 0 ,2,-4]][[x],[4],[-1]]=0 , fi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Solve the matrix equations: [(x,1)][(1, 0),(-2,-3)][(x,5)]=0

    Text Solution

    |

  17. Solve the matrix equations: [2x\ \ 3][(1, 2),(-3, 0)][(x),(8)]=0

    Text Solution

    |

  18. If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I .

    Text Solution

    |

  19. If f(x)=x^2-2x , find f(A), where A=[(0, 1, 2),( 4 ,5, 0 ),(0, 2 ,3)...

    Text Solution

    |

  20. If f(x)=x^3+4x^2-x , find f(A) , where A=[(0 ,1, 2 ),(2,-3 ,0),( 1,-...

    Text Solution

    |