Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 13

$W$ is not a vector subspace of $R^3$.

Let $v=(1,0,3)\in W$ and also $c=-3\in R$. Now, $$cv=-3(1,0,3)=(-3,0,-9)$$ which is not an element of $W$, in other words, $W$ is not closed under scalar multiplication. Hence, $W$ is not a vector subspace of $R^3$.