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

by gilabert1985
Tags: confused, span, vectors, working
 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 $x=(x_{1}, x_{2})$ in $\Re^{2}$ such that $x_{1}=1$. What is the span of S?" And here is the answer that has me so confused... "$span S = \Re^{2}$ because $(x_{1}, x_{2})=x_{1}(1, x^{-1}_{1}x_{2}$ when $x_{1}\neq0$ and $(x_{1}, x_{2})=(1, 0)-(1, -x_{2})$ when $x_{1}=0$." But I don't understand the first line... why does it say when $x_{1}\neq0$ if $x_{1}$ is supposed to be equal to 1? And in the second line, the same... why is $x_{1}=0$? So yeah, I understand they are linear combinations and all that, but for the condition given ($x_{1}=1$), I don't understand how this answer satisfies it.