So, I'm studying for my linear algebra midterm and I came up with kind of an interesting question that I pose to all of you brilliant people on physics forums. Let's say you have a linear transformation T(x)=Ax, with A being an nxm matrice. Apparently, for this equation to hold, x must be a member of ℝm. Maybe this is a ******** argument but if ℝm-1 is a subset/subspace (forgot the exact terminology) of ℝm then wouldn't the vector (2,1) in ℝ2 be (2,1,0) in ℝ3? vector operations with vectors in ℝm (or at least as far as I know) can't create vectors in ℝm+1, right? I have no idea if I really made my question clear at all, but I'm curious to hear what you guys have to say regardless.