<?xml version='1.0' encoding='UTF-8'?>
<exercise xmlns="https://spatext.clontz.org" version="0.0">
<statement>
<p>Consider the following statement.</p>
<ul><li>
The set of vectors <m>{{vecset}}</m> is linearly
{{#prompt}}in{{/prompt}}dependent.
</li></ul>
<ol>
<li> Write an equivalent statement using a vector equation.</li>
<li> Explain why your statement is true or false.</li>
</ol>
</statement>
<answer>
<p><me>\operatorname{RREF}{{matrix}}={{rref}}</me></p>
<ol>
<li>
The vector equation <m>{{veceq}}</m> has
{{#prompt}}
no
{{/prompt}}
{{^prompt}}
(infinitely-many)
{{/prompt}}
nontrivial solutions.
</li>
<li>
The set of vectors <m>{{vecset}}</m> is linearly
{{#independent}}in{{/independent}}dependent.
</li>
</ol>
</answer>
</exercise>