Home
Class 12
MATHS
If A = [[costheta,sintheta],[-sintheta,c...

If `A = [[costheta,sintheta],[-sintheta,costheta]]` then prove that `A^n = [[cosntheta,sinntheta],[-sinntheta,cosntheta]], n in N`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Evaluate the determinant: |[costheta,-sintheta],[sintheta,costheta]|

Find the inverse of the matrix : A = [(costheta,sintheta),(-sintheta,costheta)]

Evaluate |(2costheta,-2sintheta),(sintheta,costheta)|

if A=[(costheta,sintheta),(-sintheta,costheta)],then A^(2)=I is true for

Write the inverse of the matrix: {:[(costheta, sintheta),(-sintheta,costheta)]

Write the inverse of the matrix: {:[(costheta, -sintheta),(sintheta,costheta)]

If A = [(sintheta ,- costheta), (costheta, sintheta)] and B = [(costheta , sin theta),(-sintheta, cos theta)] . Compute (sin theta) A + (cos theta) B.

If A = [(costheta,-sintheta,0),(sintheta,costheta,0),(0,0,1)] verify that A(adj A) =1

The value of det [(cos theta, sintheta),(-sintheta, costheta)] is equal to

If costheta+sintheta=sqrt2costheta ,then show that costheta-sintheta=sqrt2 sintheta .

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

    Text Solution

    |

  2. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

    Text Solution

    |

  3. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  4. A complex number U = 4+2i.The value of |U| is

    Text Solution

    |

  5. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  6. Let A be the set of all 3xx3 symmetric matrices all of whoes entries...

    Text Solution

    |

  7. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

    Text Solution

    |

  8. If A is a square matrix such that A^2 = A, then write the value of (I+...

    Text Solution

    |

  9. Evaluate the following determinants: {:|(3,x),(x,1)| = |(3,2),(4,1)|

    Text Solution

    |

  10. If Delta={:|(1,2,3),(2,0,1),(5,3,8)|, write the minor of the element a...

    Text Solution

    |

  11. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

    Text Solution

    |

  12. If A = [[costheta,sintheta],[-sintheta,costheta]] then prove that A^n...

    Text Solution

    |

  13. If A = {:[(cosalpha, sinalpha),(-sinalpha, cosalpha)], A'A=I.

    Text Solution

    |

  14. Using elementary transformations find the inverse of [[2,0,-1],[5,1,0]...

    Text Solution

    |

  15. Using properties of determinants, prove that if x, y, z are different ...

    Text Solution

    |

  16. If A = {:[(1,2,3),(0,-1,4),(3,2,1)], find (A')^-1

    Text Solution

    |

  17. Solve by matrix method 2/x + 3/y + 10/z = 4 , 4/x - 6/y + 5/z = 1 , ...

    Text Solution

    |

  18. Let A = [[0,1],[0,0]] , show that (aI + bA)^n = a^nI + na^(n-1) bA, w...

    Text Solution

    |

  19. Using properties of determinants, show that: |[[(b+c)^2, a^2, a^2],[b^...

    Text Solution

    |

  20. Use product [[1,-1,2],[0,2,-3],[3,-2,4]][[-2,0,1],[9,2,-3],[6,1,-2]] t...

    Text Solution

    |