Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 42

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

The subset $W=\left\{\left(x_{1}, 1 / x_{1}, x_{3}\right) : x_{1} \text { and } x_{3} \text { are real numbers, } x_{1} \neq 0\right\}$ is not vector subspace of $R^3$ because it does not contain the zero vector.