Chapter 3.2, Problem 32E

Let $U$ and $V$ be the subspaces of $R^3$ defined by

$U=\left\{x:a^{T}x=0\right\}$ and $V=\left\{x:b^{T}x=0\right\}$,

Where

$a=\left[\begin{array}{c}1\\ 1\\ 0\end{array}\right]$ and $b=\left[\begin{array}{c}0\\ 1\\ -1\end{array}\right]$.

Demonstrate that the union, $U\cup V$, is not a subspace of $R^3$ (see Exercise $18$)