Home
Class 12
MATHS
If A = [(cosalpha, sinalpha),(-sinalpha,...

If A = `[(cosalpha, sinalpha),(-sinalpha,cosalpha)]` prove that, A`A^(')` = I. Hence, find `A^(-1)`.

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={:((cosalpha,sinalpha),(-sinalpha,cosalpha)):} , prove by mathematical induction that , A^(n)={:((cosnalpha,sinnalpha),(-sinnalpha,cosnalpha)):} where n(ge2) is a positive integer.

If tantheta=(sin alpha-cos alpha)/(sinalpha+cosalpha)1 then

If 3cos alpha-4sinalpha=5 , show that, 3sinalpha+4cosalpha=0 .

If A(cosalpha,sinalpha),B(sinalpha,-cosalpha),C(1,2) are the vertices of A B C , then as alpha varies, find the locus of its centroid.

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

(cosalpha+cosbeta)^2+(sinalpha+sinbeta)^2 =

For a real number alpha , let A(alpha) denote the matrix ((cosalpha,sinalpha),(-sinalpha,cosalpha)) . Then for real numbers alpha_(1) and alpha_(2) , the value of A(alpha_(1))A(alpha_(2)) is -

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

If sinalpha=x and tan alpha=y, prove that, 1/x^2-1/y^2=1 .

If tanalpha+secalpha=e^x ,then cosalpha equals

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

    |