Chapter 3 - Matrices - 3.5 Subspaces, Basis, Dimension, and Rank - Exercises 3.5 - Page 209: 3

$S$ is a subspace.

If $y=2x$. then $\left[\begin{array}{r}{x} \\ {y}\end{array}\right]=\left[\begin{array}{r}{x} \\ {2x}\end{array}\right]=x\left[\begin{array}{r}{1}\\ {2}\end{array}\right]$ and hence $S$ is spanned by the vector $\left[\begin{array}{r}{1}\\ {2}\end{array}\right]$ by Theorem 3.19 $S$ is a subspace.