## Elementary Linear Algebra 7th Edition

$S$ spans $R^2$.
Assume the combination $$a(2,0)+b(0,1)=(0,0).$$ We have the system \begin{align*} 2a&=0\\ b&=0. \end{align*} The above system has only the trivial solution, that is, $a=0, b=0$. Consequently, $S$ is linearly independent and since $R^2$ has the dimension $2$ then $S$ spans $R^2$.