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Confused with working out the span of a set of vectors in R^2 
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#1
Apr2712, 04:30 AM

P: 7

Hi everyone!
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. 


#2
Apr2712, 05:26 AM

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P: 4,500

The points (x_{1},x_{2}) in the lines that are confusing you are not points in S, but points in R^{2}, which it then shows how to represent as linear combinations of points in S



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