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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 ℝ

^{m}.

Maybe this is a ******** argument but if ℝ

^{m-1}is a subset/subspace (forgot the exact terminology) of ℝ

^{m}then wouldn't the vector (2,1) in ℝ

^{2}be (2,1,0) in ℝ

^{3}? vector operations with vectors in ℝ

^{m}(or at least as far as I know) can't create vectors in ℝ

^{m+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.