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I have the following problem which I don't understand... It is already solved, but there are three questions I have regarding it.

The problem says: "Let S be the set of all vectors [itex]x=(x_{1}, x_{2})[/itex] in [itex]\Re^{2}[/itex] such that [itex]x_{1}=1[/itex]. What is the span of S?"

And here is the answer that has me so confused...

"[itex]span S = \Re^{2}[/itex] because [itex](x_{1}, x_{2})=x_{1}(1, x^{-1}_{1}x_{2}[/itex] when [itex]x_{1}\neq0[/itex]

and [itex](x_{1}, x_{2})=(1, 0)-(1, -x_{2})[/itex] when [itex]x_{1}=0[/itex]."

But I don't understand the first line... why does it say when [itex]x_{1}\neq0[/itex] if [itex]x_{1}[/itex] is supposed to be equal to 1?

And in the second line, the same... why is [itex]x_{1}=0[/itex]?

So yeah, I understand they are linear combinations and all that, but for the condition given ([itex]x_{1}=1[/itex]), I don't understand how this answer satisfies it.

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# Confused with working out the span of a set of vectors in R^2

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