Home
Class 12
MATHS
If A =[[1,2,2],[2,1,2],[2,2,1]] then pro...

If `A =[[1,2,2],[2,1,2],[2,2,1]]` then prove that `A^2-4A-5I=0`.

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    SHARAM PUBLICATION|Exercise EXAMPLE|37 Videos

  • MODEL QUESTION PAPER -1

    SHARAM PUBLICATION|Exercise EXERCISE|41 Videos

Similar Questions

Explore conceptually related problems

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

If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] and C= abs[[1,2,3],[1,1,-1],[2,2,2]] then prove that A(BC)=(AB)C

If A= [[1,2,0],[0,1,3],[-2,5,3]],"then verify that" A=[[1,2,0],[0,1,3],[-2,5,3]] impliesA'=[[1,0,-2],[2,1,5],[0,3,3]] A+A' is symmetric

If A= [[1,2,0],[0,1,3],[-2,5,3]],"then verify that" A=[[1,2,0],[0,1,3],[-2,5,3]] impliesA'=[[1,0,-2],[2,1,5],[0,3,3]] A+A' is skmmetric

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

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

If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

IF A=[(1,-2,3),(0,-1,4),(-2,2,1):}] then find A^2-A

If A=[(0,1,0),(-1,0,2),(0,0,1)] , then show that A^3-A^2+I_3=[(2,-1,0),(1,2,-1),(0,0,1)]

If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1,2,3],[1,1,-1],[2,2,2]] Show that AB=AC though B '!=C .Verify that: A(B+C)=AB+AC

SHARAM PUBLICATION-MATRICES-EXAMPLE
  1. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  2. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

    Text Solution

    |

  3. If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0.

    Text Solution

    |

  4. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

    Text Solution

    |

  5. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

    Text Solution

    |

  6. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

    Text Solution

    |

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

    Text Solution

    |

  8. [[1,-2],[3,2]][[x,2],[1,y]]=[[-3,4],[-1,4]]Find x and y.

    Text Solution

    |

  9. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

    Text Solution

    |

  10. Find the inverse of the matrix [{:(2,5),(1,3):}]

    Text Solution

    |

  11. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

    Text Solution

    |

  12. Can the inverse of the following matrix be found? [[0,0,2],[3,6,0],[2,...

    Text Solution

    |

  13. Construct the matrix [a(ij)](2xx3) where a(ij)=|i-j|.

    Text Solution

    |

  14. If A=[[1,1],[2,2]] and B=[[2,1],[2,1]]find AB andBA.

    Text Solution

    |

  15. A and Bare square matrices of order n.Their product is commutative:Pro...

    Text Solution

    |

  16. Find x,y if[[3,2],[7,x]][[5,-2],[-7,y]]=[[1,0],[0,1]].

    Text Solution

    |

  17. If [[4x,x-2u],[2u+v,3v-2w]]=[[8,6],[3,5]] find x,u,v,w.

    Text Solution

    |

  18. Construct a matrix [a(ij)] of order 2xx2where a(ij)=i+2j.

    Text Solution

    |

  19. Find the adjoint of the matrix [[1,1,2],[0,1,2],[1,2,1]].

    Text Solution

    |

  20. Find the matrix which when added to [[2,-3],[-4,7]] gives [[4,-1],[3,2...

    Text Solution

    |