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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Weird linear algebra question

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