## Elementary Linear Algebra 7th Edition

$W$ is not a subspace of $R^2$.
Let $W$ be a subset of $V$ such that $W=\{(x, y) : x-y=1\}, \quad V=R^{2}.$ It is easy to see that $(0,0)\not\in W$ since $0-0=0\neq1$. Hence, $W$ is not a subspace of $R^2$.