Home
Class 12
MATHS
If A = ((4,5),(2,1)) show that, 6A^(-1) ...

If A = `((4,5),(2,1))` show that, `6A^(-1) + 5I = A`.

Text Solution

Verified by Experts

The correct Answer is:
`[(cosalpha ,- sin alpha),(sinalpha,cosalpha)]`
Promotional Banner

Topper's Solved these Questions

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTION|9 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|35 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise MULTIPLE CHOICE TYPE QUESTIONS|9 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2016|5 Videos

Similar Questions

Explore conceptually related problems

If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit matrix or order 2. Hence, find the inverse of A.

If A={:((1,4),(2,3)), show that, A^(2)-4A-5I=0 where I={:((1,0),(0,1))and 0={:((0,0),(0,0)).

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

If A=({:(1,4),(2,3):}) , then show that A^(2)-4A-5I=0 ,where I=({:(1,0),(0,1):}) " and " O=({:(0,0),(0,0):}) .

If A={:((1,2),(-3,0)), show that, A^(2)+3A+5I={:((3,8),(-12,-1)).

If A = ([1,4],[2,3]) then show that A^2-4A-5I = theta and using this find A^(-1) . Where I= ([1,0],[0,1]) and theta = ([0,0],[0,0]) .

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

If A = [[3,-5],[-4,2]] ,show that A^2 -5A-14I =0.

If A = [[4,5],[5,6]] , show that A^2 = 10A + I where I is the unit matrix of order 2.

If A=({:(2,-1),(1,3):}) , then show that A^2-5A+7I_2=0 : hence find A^(-1) .

CHHAYA PUBLICATION-ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD-VERY SHORT ANSWER TYPE QUESTIONS
  1. Find the inverse of matrices using elementary column transformations: ...

    Text Solution

    |

  2. Find the inverse of matrices using elementary column transformations: ...

    Text Solution

    |

  3. Find the inverse of matrices using elementary column transformations: ...

    Text Solution

    |

  4. If A =[(5,-8),(-5,8)], show by elementary row transformations that A^...

    Text Solution

    |

  5. If B = [(-2,2,1),(0,4,5),(-2,6,6)], show by elementary row operations ...

    Text Solution

    |

  6. If A = [(1,-2,3),(1,2,1),(-1,2,-3)] show by elementary colomn operatio...

    Text Solution

    |

  7. If A =[(2,2),(4,3)] show that, AA^(-1) =I(2) wher I(2) is the unit mat...

    Text Solution

    |

  8. Find the matrix A when A^(-1) = (1)/(11)[(1,4),(-2,3)]

    Text Solution

    |

  9. Find the matrix A when A^(-1) = [(cos theta,sin theta),(-sin theta,...

    Text Solution

    |

  10. If A =((3,1),(0,2)) show that (A^(T))^(-1) = (A^(-1))^(T) where A^(T) ...

    Text Solution

    |

  11. If A =[(2,5),(1,3)] and AB = [(-13,8),(-8,5)], find B.

    Text Solution

    |

  12. If A = ((4,5),(2,1)) show that, 6A^(-1) + 5I = A.

    Text Solution

    |

  13. If A = [(cosalpha, sinalpha),(-sinalpha,cosalpha)] prove that, AA^(') ...

    Text Solution

    |

  14. If A =[(1,-tan""(theta)/(2)),(tan""(theta)/(2), 1)] and B = [(1,tan""(...

    Text Solution

    |

  15. If A = [(-3,-4),(4,5)] and B = [(2,-3),(5,-8)], verify that (AB)^(-1) ...

    Text Solution

    |

  16. If A = [(2,1),(3,4)] and B = [(1,-2),(-1,1)], find the value of (AB)^(...

    Text Solution

    |

  17. If A = ((3,1),(-1,2)), I = ((1,0),(0,1)) and O = ((0,0),(0,0)) show th...

    Text Solution

    |

  18. If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit ma...

    Text Solution

    |

  19. Show that the matrix A= [(2,-3),(3,4)] satisfies the equation x^(2) - ...

    Text Solution

    |

  20. Show that, the matrix A = [(1,2,2),(2,1,2),(2,2,1)] satisfies the equa...

    Text Solution

    |