So I have 2 questions that both ask to describe a set span geometrically...
Show that $span((1,2))$ does not $= R^2$. Describe the set $span ((1,2)) $geometrically.
If u $\in R^2$, describe the set span (U) geometrically. (Hint: Do not forget a very special case).
I believe I'm trying to describe the shape of the span(Is that what this question is asking?), but I don't understand how you do that. When trying to figure this out, I've read that "One vector spans a line. Two linearly independent vectors span a plane. And ≥3 linearly independent vectors span a hyper-plane." So do I use on of these ideas to describe it? Could some please explain how you describe a set span geometrically?
Also with question one, how do you prove a span is not in $R^2$? I understand how to prove something is in $R^2$, but not when it's not. Could some also please explain how you would do that?