Chapter 4 - Vector Spaces - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 16

$S$ does not span $R^2$.

Since all the vectors of $S$ are just a scalar multiple of the vector $(1,2)$. Then, $S$ does not span $R^2$. It just spans a subspace consisting of all vectors in the direction or in the opposite direction of the vector $(1,2)$.