## Elementary Linear Algebra 7th Edition

$W$ is not a vector subspace of $R^3$.
Let $W=\left\{\left(x_{1}, x_{2}, 4\right) : x_{1} \text { and } x_{2} \text { are real numbers }\right\}$, $u=(1,2,4)\in W$ and $c=2\in R$, then \begin{align*} cu&=2(1,2,4)\\ &=(2,4,8)\not\in W. \end{align*} Hence, $W$ is not a vector subspace of $R^3$.