Results 1 to 3 of 3

Math Help - help needed with a proof

  1. #1
    Junior Member
    Joined
    Mar 2006
    From
    Manchester
    Posts
    25

    help needed with a proof

    Suppose that

    M={(a b ;a,b,c belong to R
    -b c)

    and N={(x 0 ;x,y belong to R
    y 0)

    are subspaces of M2R. Show that (M:R) + (N:R) = ((M'intersect'N):R) + ((M+N):R)

    Cheers, Shaun
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Shaun Gill View Post
    Suppose that

    M={(a b ;a,b,c belong to R
    -b c)

    and N={(x 0 ;x,y belong to R
    y 0)

    are subspaces of M2R. Show that (M:R) + (N:R) = ((M'intersect'N):R) + ((M+N):R)

    Cheers, Shaun
    I presume,
    M+N=M\cup B
    This looks like the principle of inclusion-exlusion.
    Thus,
    |M + N|=|M|+|N|-|M\cap N|
    Thus,
    |M + N|+|M\cap N|=|M|+|N|
    So dimensions are,
    (M+N:R)+(M\cap N:R)=(M:R)+(N:R)
    I believe that is the idea.

    But the sad thing is I do not know how to generalize this to infinite fields. So far this confirms what you said for finite fields.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    I think that these are the same problem.
    http://www.mathhelpforum.com/math-he...ons-basis.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A proof is needed
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 25th 2010, 03:59 PM
  2. A proof is needed
    Posted in the Geometry Forum
    Replies: 3
    Last Post: June 6th 2010, 02:39 AM
  3. 'Proof' help needed please...
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: February 27th 2010, 12:39 PM
  4. Analysis proof help needed
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: October 13th 2008, 10:59 AM
  5. A much needed proof
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 10th 2007, 10:05 AM

Search Tags


/mathhelpforum @mathhelpforum