Home
Class 12
MATHS
Show that the matrix A=[[1 ,2, 2],[ 2, 1...

Show that the matrix `A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]]` satisfies the equation `A^2-4A-5I_3=O` and 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

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and 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) .

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

Show that A=[(-8, 5),( 2, 4)] satisfies the equation A^2+4A-42 I=O . Hence, find A^(-1) .

If A[{:(2,3),(1,2):}] satisfy the equation A^2-kA+I=0 , then find k also A^(-1) .

Show that A=|[2,-3], [3 ,4]| satisfies the equation x^2-6x+17=0 . Hence, find A^(-1) .

A=[{:(1,3),(2,1):}] satisfy the equation A^2-kA-5I=0 , then find k and also A^(-1) .

Show that the matrix A=[2 3 1 2] satisfies the equation A^2-4A+I=0

Find x and y i the matrix A= 1/3 [[1,2,2],[2,1,-2],[x,2,y]] satisfythe condition A A\'=A\'A=I_3

Find the rank of the matrix A = [[0,1,2,-2],[4,0,2,6],[2,1,3,1]]

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. For the matrix A=|[3, 1], [7, 5]| , find x and y so that A^2+x I=y Ado...

    Text Solution

    |

  2. For the matrix A=[[3, 2],[ 1, 1]] , find the numbers a and b such that...

    Text Solution

    |

  3. Show that the matrix A=[[1 ,2, 2],[ 2, 1, 2],[ 2, 2, 1]] satisfies the...

    Text Solution

    |

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

    Text Solution

    |

  5. Find a 2xx2 matrix B such that B[(1,-2),( 1, 4)]=[(6, 0),( 0, 6)] .

    Text Solution

    |

  6. Find the matrix A satisfying the matrix equation [(2, 1),( 3, 2)]A...

    Text Solution

    |

  7. Find the matrix X for which [(1,-4) ,(3,-2)]X=[(-16,-6),( 7, 2)] .

    Text Solution

    |

  8. If A=[[0 ,1 ,3],[ 1, 2,x],[2, 3, 1]] and A^(-1)=[[1//2,-4 ,5//2],[-1//...

    Text Solution

    |

  9. If A=[[cosalpha,sinalpha],[-sinalpha,cosalpha]] is such that A^T=A^(-1...

    Text Solution

    |

  10. If matrix A=[(0, 2,y),( z, x, y),(-z, x-y, z)] satisfies A^T=A^(-1) ...

    Text Solution

    |

  11. Find the matrix A such that |A|=2 and a d j\ A=[[2, 2, 0],[ 2, 5, 1],[...

    Text Solution

    |

  12. If A is a non-singular matrix, prove that: a d j\ (A) is also no...

    Text Solution

    |

  13. If A is a non-singular matrix, prove that (a d j\ A)^(-1)=(a d j\ A...

    Text Solution

    |

  14. Find the non-singular matrices A , if it is given that a d j\ (A)=[...

    Text Solution

    |

  15. If A=[(2,-1, 1),(-1, 2,-1),( 1,-1, 2)] , find (a d j\ A)^(-1) and (a...

    Text Solution

    |

  16. Let A be a non-singular matrix. Show that A^T A^(-1) is symmetric i...

    Text Solution

    |

  17. Find the adjoint of the following matrices: [(-3, 5),( 2, 4)] Verif...

    Text Solution

    |

  18. Find the adjoint of the following matrices: [(cosalpha,sinalpha),(si...

    Text Solution

    |

  19. Compute the adjoint of each of the following matrices: [[1, 2, 2],[ ...

    Text Solution

    |

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

    Text Solution

    |