1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I'm lost!

  1. Oct 2, 2005 #1

    hgj

    User Avatar

    I need to do the following question:
    Let W be the additive subgroup of R[tex]^m[/tex] of solutions of a system of homogeneous equations AX=0. Show that the solutions of an inhomogeneous system AX=B forms a coset of W.

    I really just don't know where to start. Any help would be appreciated.
     
  2. jcsd
  3. Oct 2, 2005 #2

    hgj

    User Avatar

    Okay, here's what I have now:
    Let T be a solution of AX=B. Then W+T is the set of solutions of AX=B. So AT=B. Then AX=AT [tex]<=>[/tex] A(X-T)=0 [tex]<=>[/tex] X-T [tex]\in[/tex] W [tex]<=> [/tex] X [tex]\in[/tex] W+T

    I think I don't fully understand the definition of coset, so I'm not sure what to do from here. Our definition is :
    A left coset is a subbset of the form aH={ah s.t. h is in H} for any subgroup H of a group G.
     
  4. Oct 2, 2005 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    But this said 'Let W be the additive subgroup of Rm'!!

    Your cosets are defined by a+H={a+h s.t. h is in H}
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: I'm lost!
  1. I'm very lost (Replies: 4)

  2. Help I'm lost (Replies: 2)

  3. I'm Lost (Replies: 13)

  4. I'm lost. Help? (Replies: 5)

  5. I'm really lost (Replies: 10)

Loading...