Course: Linear Algebra

So I have the set $\displaystyle \left\{(0,0) , (1,3)\right\}$ which I will call S.

I'll have the system:

$\displaystyle c_2 = x_1$

$\displaystyle 3c_2 = x_2$

Which gives me $\displaystyle c_2 = x_1 = \frac{1}{3}x_2$

Can this mean that span(S) = R2?

Is the zero vector redundant?