Solving an Inhomogeneous System: A Coset of W in R^m

[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.

 

[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.

 

[HallsofIvy]

But this said 'Let W be the additive subgroup of R^m'!

Your cosets are defined by a+H={a+h s.t. h is in H}