Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 10

$W$ is not a vector subspace of $R^2$.

Let $u=(1,2)\in W$, so the components of $u$ are integer but the vector $\frac{1}{2}u=\frac{1}{2}(1,2)=(\frac{1}{2},1)$ has components which are not integer. Hence $W$ is not vector subspace of $R^2$.