Results 1 to 3 of 3

Math Help - Proving a subgroup relation

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    66

    Post Proving a subgroup relation

    Here is the question: Let

    H = 2x2 matrix with entries
    |cosA -sinA |
    |sinA cosA|
    and prove H is a subgroup of SL2(R)
    Showing the inverse is an element isnt a problem im having a problem showing closure(havent attempted inverse yet)

    I let A,B element of H then u get 2 matrices with those entries and A and B as measures then i get
    AB = |cosAcosB - sinAsinB -cosAsinB -sinAcosB|
    |sinAcosB + cosAsinB -sinAsinB + cosAcosB|

    then det(AB) =
    (cosAcosB - sinAsinB)(-sinAsinB + cosAcosB) - (-cosAsinB - sinAcosB)(sinAcosB + cosAsinB)

    when you multiply it all out i get abunch of cosAcosBsinAsinB terms that cancel off a cos(squared)Acos(squared)B and sin(squared)Asin(squared)B that add to 1 and then i get 2 other terms a cos(squared)Asin(squared)B and sin(squared)Acos(squared)B. I know that the det = 1 is there some identity with the other 2 terms im missing or did i make a mistake somewhere else. Thanks in advance for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by ChrisBickle View Post
    Here is the question: Let

    H = 2x2 matrix with entries
    |cosA -sinA |
    |sinA cosA|
    and prove H is a subgroup of SL2(R)
    Showing the inverse is an element isnt a problem im having a problem showing closure(havent attempted inverse yet)

    I let A,B element of H then u get 2 matrices with those entries and A and B as measures then i get
    AB = |cosAcosB - sinAsinB -cosAsinB -sinAcosB|
    |sinAcosB + cosAsinB -sinAsinB + cosAcosB|

    then det(AB) =
    (cosAcosB - sinAsinB)(-sinAsinB + cosAcosB) - (-cosAsinB - sinAcosB)(sinAcosB + cosAsinB)

    when you multiply it all out i get abunch of cosAcosBsinAsinB terms that cancel off a cos(squared)Acos(squared)B and sin(squared)Asin(squared)B that add to 1 and then i get 2 other terms a cos(squared)Asin(squared)B and sin(squared)Acos(squared)B. I know that the det = 1 is there some identity with the other 2 terms im missing or did i make a mistake somewhere else. Thanks in advance for your help.

    this seems to be basic trigonometry: for ex. cosAcosB - sinAsinB = cos(A+B)...check your trigonometric identities.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    66
    Thank you for your help.

    Chris
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] QM- Proving the uncertainty relation - Commutators
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: April 8th 2011, 10:12 AM
  2. Replies: 2
    Last Post: March 2nd 2011, 08:07 PM
  3. Replies: 4
    Last Post: April 27th 2010, 07:57 AM
  4. Subgroup of S_n, relation and 1-1 correspondance
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 10th 2009, 07:35 AM
  5. Proving a subgroup relation
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 18th 2009, 02:42 PM

Search Tags


/mathhelpforum @mathhelpforum