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   <h2 class="likechapterHead"><a 
 id="x15-19000"></a>Chapter SLE&#x00A0;&#x00A0;Systems of Linear Equations</h2>
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</p><!--l. 10--><p class="indent" >   We will motivate our study of linear algebra by studying solutions to
systems of linear equations. While the focus of this chapter is on the
practical matter of how to find, and describe, these solutions, we will
also be setting ourselves up for more theoretical ideas that will appear
later.
                                                                          

                                                                          
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   <div class="likesectionTOCS">
   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-20000">Section WILA What is Linear Algebra?</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-21000" id="QQ2-16-21">Subsection LA: &#x201C;Linear&#x201D; + &#x201C;Algebra&#x201D;</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-22000" id="QQ2-16-22">Subsection AA: An Application</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-23000" id="QQ2-16-23">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-24000" id="QQ2-16-24">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li15.xml#x16-25000" id="QQ2-16-25">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-26000">Section SSLE Solving Systems of Linear Equations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-27000" id="QQ2-17-27">Subsection SLE: Systems of Linear Equations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-28000" id="QQ2-17-28">Subsection PSS: Possibilities for Solution Sets</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-29000" id="QQ2-17-29">Subsection ESEO: Equivalent Systems and Equation Operations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-30000" id="QQ2-17-30">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-31000" id="QQ2-17-31">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li16.xml#x17-32000" id="QQ2-17-32">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-33000">Section RREF Reduced Row-Echelon Form</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-34000" id="QQ2-18-34">Subsection MVNSE: Matrix and Vector Notation for Systems
of Equations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-35000" id="QQ2-18-35">Subsection RO: Row Operations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-36000" id="QQ2-18-36">Subsection RREF: Reduced Row-Echelon Form</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-37000" id="QQ2-18-37">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-38000" id="QQ2-18-38">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li17.xml#x18-39000" id="QQ2-18-39">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-40000">Section TSS Types of Solution Sets</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-41000" id="QQ2-19-41">Subsection CS: Consistent Systems</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-42000" id="QQ2-19-42">Subsection FV: Free Variables</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-43000" id="QQ2-19-43">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-44000" id="QQ2-19-44">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li18.xml#x19-45000" id="QQ2-19-45">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-46000">Section HSE Homogeneous Systems of Equations</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-47000" id="QQ2-20-47">Subsection SHS: Solutions of Homogeneous Systems</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-48000" id="QQ2-20-48">Subsection NSM: Null Space of a Matrix</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-49000" id="QQ2-20-49">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-50000" id="QQ2-20-50">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li19.xml#x20-51000" id="QQ2-20-51">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;<span class="likesectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-52000">Section NM Nonsingular Matrices</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-53000" id="QQ2-21-53">Subsection NM: Nonsingular Matrices</a></span>
                                                                          

                                                                          
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-54000" id="QQ2-21-54">Subsection NSNM: Null Space of a Nonsingular Matrix</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-55000" id="QQ2-21-55">Subsection READ: Reading Questions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-56000" id="QQ2-21-56">Subsection EXC: Exercises</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-57000" id="QQ2-21-57">Subsection SOL: Solutions</a></span>
<br />   &#x00A0;&#x00A0;<span class="likesubsectionToc" ><a 
href="fcla-xml-1.31li20.xml#x21-58000" id="QQ2-21-58">Annotated Acronyms SLE: Systems of Linear Equations</a></span>
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