## Elementary Linear Algebra 7th Edition

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