Hm... I was about to ask the following:
OK, so, then, let $\mathbf{v}_1$, and $\mathbf{v}_2$ be linearly independent, can I safely say that that $\text{span}(\mathbf{v}_1, \mathbf{v}_2)$ equal to $R^2$?
But now I'm thinking that because they are linearly independent, we can find any values $c_1$, $c_2$, such that the equation $(x, y) = c_1\mathbf{v}_1 + c_2\mathbf{v}_2$, holds true.