Chapter 4 - Vector Spaces - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 23

$S$ does not span $R^3$.

Since $R^3$ has the dimension $3$ and $S$ has only two vectors, then $S$ does not span $R^3$. $S$ spans only two-dimensional subspace of $R^3$. Moreover, this subspace is a plane contains the vectors of $S$.