<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<p>Consider the following two sets of Euclidean vectors:
</p>
<me>
U={{U}} \hspace{2em} W={{W}}
</me>
<p> Explain why one of these sets is a subspace of <m>\mathbb{R}^{{dim}}</m> and one is not.
</p>
</statement>
<answer>
<p><m>{{subspace}}</m> is a subspace of <m>\mathbb{R}^{{dim}}</m> and <m>{{nonsubspace}}</m> is not.</p>
</answer>
</exercise>