Chapter 4 - Vector Spaces - Review Exercises - Page 221: 22

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

Let $W$ be a subset of $V$ such that $$W=\{(x, y, z) : x \geq 0\}, \quad V=R^{3}.$$ $W$ is not a subspace of $R^3$ since it is not closed under scalar multiplication. For example, $u=(1,2,0)\in W$ and $-2u=-2(1,2,0)=(-2,-4,0)\not \in W$.