# Homework Help: I'm lost!

1. Oct 2, 2005

### hgj

I need to do the following question:
Let W be the additive subgroup of R$$^m$$ 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. Oct 2, 2005

### hgj

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 $$<=>$$ A(X-T)=0 $$<=>$$ X-T $$\in$$ W $$<=>$$ X $$\in$$ 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.

3. Oct 2, 2005

### HallsofIvy

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}