Home
Class 12
MATHS
Show that the matrix A=[[2, 3],[ 1, 2...

Show that the matrix `A=[[2, 3],[ 1, 2]]` Satisfies the equation `A^2-4 A+I=O`, where `I` is `2 xx 2` identity matrix and `O` is `2 xx 2` zero matrix. Using this equation, find `A^(-1)`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    V PUBLICATION|Exercise QUESTION BANK|168 Videos

  • DIFFERENTIAL EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|149 Videos

Similar Questions

Explore conceptually related problems

Consider the matrix A=[[3,1],[-1,2]] Find A^2

Consider the matrix A=[[2,5],[3,2]] Find A^-1

Consider the matrix A=[[2,5],[3,2]] Find adj(A)

Consider the matrix A=[(-8,5),(2,4)] Show that 'A' satisfies the equation x^2+4x-42=0

Consider the matrix A=[[3,-2],[4,-2]] Find A^2

show that the matrix A= [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric matrix

Consider the matrix A=[[3,1],[-1,2]] Find k so that A^2=kA-7I

Consider the matrix A=[[3,-2],[4,-2]] find k so that A^2=kA-2I

For the matrix A= [[3,2],[1,1]] ,find the numbers a and b such that A^2+aA+bI=0

Find the inverse of the matrix A=[[2,3],[-1,5]] using row transformation.

V PUBLICATION-DETERMINANT-QUESTION BANK
  1. If Delta=|[a(11), a(12 ), a(13)], [a(21), a(22), a(23)],[ a(31) , a...

    Text Solution

    |

  2. If A=[[2, 3],[ 1, -4]] and B=[[1, -2],[ -1, 3]], then verify tha...

    Text Solution

    |

  3. Show that the matrix A=[[2, 3],[ 1, 2]] Satisfies the equation A^2-...

    Text Solution

    |

  4. Find the adjoint of each of the matrices [[1 , 2],[ 3, 4]]

    Text Solution

    |

  5. Find the adjoint of the matrix [[1 , -1, 2],[ 2, 3, 5],[ -2, 0, ...

    Text Solution

    |

  6. Verify A (adj A)=(adj A)A=|A|I in the following matrices. [[2,3],[-4,-...

    Text Solution

    |

  7. Find the inverse of the following matrics. [[2,-2],[4,3]]

    Text Solution

    |

  8. Find the inverse of the following matrics. [[-1,5],[-3,2]]

    Text Solution

    |

  9. Find the inverse of each of the matrices [[1, 2, 3],[ 0, 2, 4],[...

    Text Solution

    |

  10. Find the inverse of the following A=[[1,0,0],[3,3,0],[5,2,-1]]

    Text Solution

    |

  11. Find the inverse of each of the matrices [[2 , 1 , 3],[ 4, -1, 0],[...

    Text Solution

    |

  12. Find the inverse of the following A=[[1,-1,2],[0,2,-3],[3,-2,4]]

    Text Solution

    |

  13. Find the inverse of each of the matrices. [[1, 0, 0],[ 0 , cos alph...

    Text Solution

    |

  14. Let A=[[3 , 7],[ 2, 5]] and B=[[6 , 8],[ 7, 9]] Verify that (A B)...

    Text Solution

    |

  15. If A =[[3,1],[-1,2]],show that A^2-5A + 7I=0 Hence, find A^(-1)

    Text Solution

    |

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

    Text Solution

    |

  17. For the matrix A=[[1,1,1],[1,2,-3],[2,-1,3]] show that A^3-6A^2+5A+11I...

    Text Solution

    |

  18. Let A be a non-singular square matrix of order 3xx3.Then |adj A| is .....

    Text Solution

    |

  19. If A is an invertible matrix of order 2, then det(A^(-1))=

    Text Solution

    |

  20. Solve the system of equations '2 x+5 y=1' '3 x+2 y=7'

    Text Solution

    |