Home
Class 12
MATHS
If A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)] ...

If `A=[(1, 2, 0 ),(3,-4, 5),( 0,-1, 3)]` , compute `A^2-4A+3I_3` .

Text Solution

Verified by Experts

Given that,
`A=[(1,2, 0), (3,-4, 5),( 0,-1, 3)]`
we have to find,
`A^2-4A+3I_3`
so,`A^2=[(1,2, 0), (3,-4, 5),( 0,-1, 3)]xx[(1,2, 0), (3,-4, 5),( 0,-1, 3)]`
`=[(1+6,2-8,10),(3-12,6+16-5,-20+15),(-3,4-3,-5+9)]`
`=[(7,-6,10),(-9,17,-5),(-3,1,4)]`
`A^2-4A+3I_3`
...
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,-3,4),(2,-3,4),(0,-1,1)] , then :

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

Given A=[{:(5,0,4),(2,3,2),(1,2,1):}] , B^(-1)=[{:(1,2,3),(1,4,3),(1,3,4):}] . Compute (AB)^(-1) .

If A=[{:(2," "3,-5),(0,-1," "4):}] , verify that (3A)'=3A'.

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

If A=[(-1,1,0),(0,-1,1),(2,3,4)] verify that 3/4A'=(3/4A)^'

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

If A=[[1,2,3]], B=[(-5,4,0),(0,2,-1),(1,-3,2)] then (A) AB=[(-2),(-1),(4)] (B) AB=[-2,-1,4] (C) AB=[4,-1,2] (D) AB=[(-5,4,0),(0,4,-2),(3,-9,6)]

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

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. Solve the matrix equations: [(0, 2, 1)][(1, 2, 0),( 2 ,0 ,1 ),(1 ,0...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. If A=[(1 ,0, 2), (0, 2, 1), (2, 0, 3)] , then show that A is a root of...

    Text Solution

    |

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

    Text Solution

    |

  8. If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I3=O .

    Text Solution

    |

  9. Without using the concept of inverse of a matrix, find the matrix [...

    Text Solution

    |

  10. Find the matrix A such that : [(1 ,0 ),(0 ,1)]A=[(3 ,3 ,5 ),(1, 0 ,1)]

    Text Solution

    |

  11. Find the matrix A such that : [2, 1, 3][(-1,0,-1),(-1,1 ,0 ),(0 ,1, 1...

    Text Solution

    |

  12. Find a 2xx2 matrix A such that A[(1,-2),( 1, 4)]=6I2 .

    Text Solution

    |

  13. If A=[(0, 0), (4, 0)] , find A^(16) .

    Text Solution

    |

  14. If A=[(0,-x),(x,0)] , B=[(0 ,1 ),(1 ,0)] and x^2=-1 , then show tha...

    Text Solution

    |

  15. If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I...

    Text Solution

    |

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

    Text Solution

    |

  17. If P(x)=[cosxsinx-sinxcosx] , then show that P(x)\ P(y)=P(x+y)=P(y)\ P...

    Text Solution

    |

  18. If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...

    Text Solution

    |

  19. If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...

    Text Solution

    |

  20. If A=[(1 ,1),( 0, 1)] , prove that A^n=[(1,n),(0, 1)] for all positive...

    Text Solution

    |