Home
Class 12
MATHS
For the matrix A=[1 1 1 1 2-3 2-1 3] . S...

For the matrix `A=[1 1 1 1 2-3 2-1 3]` . Show that `A^3-6A^2+5A+11\ I_3=O` . Hence, find `A^(-1)` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos

Similar Questions

Explore conceptually related problems

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

If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find A^(-1) .

If A=[(3, 1),( 1, 2)] , show that A^2-5A+5I=0 . Hence, find A^(-1) .

For the matrix A=[[3 ,1],[ 7, 5]], find x and y sot that A^2+x I+y Adot=0 Hence, Find A^(-1)dot

For the matrix A=[[1,-1, 1],[ 2 ,3, 0 ],[18 ,2 ,10]] , show that A(a d j\ A)=O .

For the matrix A=[[3, 2],[ 1, 1]] , find the numbers a and b such that A^2+a A+b I=O . Hence, find A^(-1) .

If A=[(2,-3),(3,4)], show the A^2-6A+17I=0. Hence find A^-1

For the matrix A=[{:(,3,2),(,1,1):}] Find a & b so that A^(2)+aA+bI=0 . Hence find A^(-1)

If A=[{:(1,-1),(2,3):}] , shown that A^(2)-4A+5I=o . Hence Find A^(-1) .

Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies the equation, A^3-A^2-3A-I_3=O . Hence, find A^(-1) .

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. Show that A=[(5, 3),(-1,-2)] satisfies the equation x^2-3x-7=0 . Thus,...

    Text Solution

    |

  2. Show that A=[(6, 5),( 7, 6)] satisfies the equation x^2-12 x+1=0 . Thu...

    Text Solution

    |

  3. For the matrix A=[1 1 1 1 2-3 2-1 3] . Show that A^3-6A^2+5A+11\ I3=O ...

    Text Solution

    |

  4. Show that the matrix, A=[[1, 0,-2],[-2,-1, 2],[ 3, 4, 1]] satisfies th...

    Text Solution

    |

  5. If A=[2-1 1-1 2-1 1-1 2] . Verify that A^3-6A^2+9A-4I=O and hence find...

    Text Solution

    |

  6. If A=1/9[-8 1 4 4 4 7 1-8 4] , prove that A^(-1)=A^T .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Solve the matrix equation [[5 ,4] ,[1 ,1]]X=[[1,-2],[ 1 ,3]] , where...

    Text Solution

    |

  10. Find the matrix X satisfying the matrix equation: X[[5, 3],[-1,-2]]=...

    Text Solution

    |

  11. Find the matrix X for which: [(3, 2), (7, 5)]X[(-1, 1),(-2, 1)]=[(2,-...

    Text Solution

    |

  12. Find the matrix X satisfying the equation: [[2, 1 ],[5, 3]]X[[5, 3],...

    Text Solution

    |

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

    Text Solution

    |

  14. If A is a square matrix of order n , prove that |A\ a d j\ A|=|A|^n...

    Text Solution

    |

  15. If A^(-1)=[3-1 1-15 6-5 5-2 2]and B=[1 2-2-1 3 0 0-2 1], find (A B)^(-...

    Text Solution

    |

  16. If A=[[1, -230] ,[-14, -221]] , find (A^ T) .

    Text Solution

    |

  17. Find the adjoint of the matrix A=[(-1,-2,-2), (2 ,1...

    Text Solution

    |

  18. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

    Text Solution

    |

  19. Use elementary column operation C2 -> C2 -2C1 in the matrix equati...

    Text Solution

    |

  20. Apply elementary transformation R2->R2-3R1 in the matrix equation ...

    Text Solution

    |