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Homework Help: I'm lost!

  1. Oct 2, 2005 #1

    hgj

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    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

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    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

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    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}
     
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