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		<title>Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations</title>
		<link>https://yutsumura.com/possibilities-of-the-number-of-solutions-of-a-homogeneous-system-of-linear-equations/</link>
				<comments>https://yutsumura.com/possibilities-of-the-number-of-solutions-of-a-homogeneous-system-of-linear-equations/#respond</comments>
				<pubDate>Sun, 24 Jul 2016 04:42:11 +0000</pubDate>
		<dc:creator><![CDATA[Yu]]></dc:creator>
				<category><![CDATA[Linear Algebra]]></category>
		<category><![CDATA[homogeneous system]]></category>
		<category><![CDATA[linear algebra]]></category>
		<category><![CDATA[linear equations]]></category>
		<category><![CDATA[quiz]]></category>
		<category><![CDATA[true or false]]></category>

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<p>The post <a href="https://yutsumura.com/possibilities-of-the-number-of-solutions-of-a-homogeneous-system-of-linear-equations/" target="_blank">Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations</a> first appeared on <a href="https://yutsumura.com/" target="_blank">Problems in Mathematics</a>.</p>]]></description>
								<content:encoded><![CDATA[<h2> Problem 14</h2>
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                                <p>If a homogeneous system of linear equations has a nontrivial solution, then the system has infinitely many solutions.</p>
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                                    <p>Way to go! The possibility of the number of solutions of any system of linear equations are zero, one, or infinity.<br />
Since a homogeneous system has the zero solution, if it has non-trivial solutions, it has two solutions. Hence there should be infinitely many solutions.</p>                                </div>
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                                    <p>Review the following fact: the possibility of the number of solutions of any system of linear equations are zero, one, or infinity.<br />
Since a homogeneous system has the zero solution, if it has non-trivial solutions, it has two solutions. Hence there should be infinitely many solutions.</p>
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<button class="simplefavorite-button has-count" data-postid="148" data-siteid="1" data-groupid="1" data-favoritecount="41" style="">Click here if solved <i class="sf-icon-star-empty"></i><span class="simplefavorite-button-count" style="">41</span></button><p>The post <a href="https://yutsumura.com/possibilities-of-the-number-of-solutions-of-a-homogeneous-system-of-linear-equations/" target="_blank">Possibilities of the Number of Solutions of a Homogeneous System of Linear Equations</a> first appeared on <a href="https://yutsumura.com/" target="_blank">Problems in Mathematics</a>.</p>]]></content:encoded>
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