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

Verified by Experts

Given that,
`A=[(3,-2),( 4,-2)]`
and `I=[(1 ,0),( 0 ,1)]`
`A^2=A*A`
`=[(3,-2),( 4,-2)][(3,-2),( 4,-2)]`
`=[(9-8,-6+4),(12-8,-8+4)]`
`=[(1,-2),(4,-4)]`
`=A^2-A+2I`
`=[(1,-2),(4,-4)]-[(3,-2),( 4,-2)]+2[(1 ,0),( 0 ,1)]`
`=[(1,-2),(4,-4)]-[(3,-2),( 4,-2)]+[(2,0),( 0 ,2)]`
`=[(0,0),(0,0)]`
`therefore A^2-A+2I=0`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

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

If A=[(5,2),(-1,2)] and I=[(1,0),(0,1)] show that : (A-3I)(A-4I)=O

If A=[[1,2,22,1,22,2,1]], 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=[(4,2),(-1,1)] , show that (A-2 I) A-3 I) =0

If A=[[1,0,20,2,12,0,3]], prove that A^(3)-6A^(2)+7A+2I=0

If A= [{:(2, -5), (0, 1):}]" and I" = [{:(1, 0), (0, 1):}] then find the matrix X such that 4A-2X + I = O.

if A=[[1,2,33,2,14,-2,1]] then prove that A^(3)-23A-40I=0

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [(x,4,1)][(2,1,2),(1,0,2),(0,2,-4)][(x),(4),(-1)]=0 , find xdot

    Text Solution

    |

  2. If [(1, -1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0 , fin...

    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+7I2=O .

    Text Solution

    |

  6. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I2=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)] is a root of the equation A...

    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-2I2=0 .

    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. If A=[(2, 3),( 1, 2)] and I=[(1, 0),( 0, 1)] , then find lambda,mu ...

    Text Solution

    |

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

    Text Solution

    |

  16. Solve the matrix equations: [(0, 2, 1)][(1, 2, 0),( 2 ,0 ,1 ),(1 ,0...

    Text Solution

    |

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

    Text Solution

    |

  18. If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] , compute A^2-4A+3I3 .

    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

    |