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<text>LE3 ver. 100</text>
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<text><div class="stx"><div class="stx-knowl">
<div class="stx-intro"><p> Consider each of the following systems of linear equations or vector equations. </p></div>
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<li><div class="stx-knowl">
<div class="stx-intro"><p><span class="math display-math" data-latex="\begin{matrix} 2 \, x_{1} &amp; - &amp; 6 \, x_{2} &amp; - &amp; 3 \, x_{3} &amp; = &amp; 0 \\ -x_{1} &amp; + &amp; 3 \, x_{2} &amp; + &amp; 2 \, x_{3} &amp; = &amp; -2 \\ 3 \, x_{1} &amp; - &amp; 9 \, x_{2} &amp; + &amp; x_{3} &amp; = &amp; -3 \\ 11 \, x_{1} &amp; - &amp; 33 \, x_{2} &amp; + &amp; x_{3} &amp; = &amp; -13 \\ \end{matrix}">\[\begin{matrix} 2 \, x_{1} &amp; - &amp; 6 \, x_{2} &amp; - &amp; 3 \, x_{3} &amp; = &amp; 0 \\ -x_{1} &amp; + &amp; 3 \, x_{2} &amp; + &amp; 2 \, x_{3} &amp; = &amp; -2 \\ 3 \, x_{1} &amp; - &amp; 9 \, x_{2} &amp; + &amp; x_{3} &amp; = &amp; -3 \\ 11 \, x_{1} &amp; - &amp; 33 \, x_{2} &amp; + &amp; x_{3} &amp; = &amp; -13 \\ \end{matrix}\]</span></p></div>
<ol>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain and demonstrate how to find a simpler linear system that has the same solution set. </p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain whether this solution set has no solutions, one solution, or infinitely-many solutions. If the set is finite, describe it using set notation. </p></div>
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</ol>
</div></li>
<li><div class="stx-knowl">
<div class="stx-intro"><p><span class="math display-math" data-latex="x_{1} \left[\begin{array}{c} 1 \\ 0 \\ 2 \\ 7 \end{array}\right] + x_{2} \left[\begin{array}{c} 2 \\ 0 \\ 4 \\ 14 \end{array}\right] + x_{3} \left[\begin{array}{c} 2 \\ 1 \\ 3 \\ 14 \end{array}\right] = \left[\begin{array}{c} -4 \\ -1 \\ -7 \\ -28 \end{array}\right]">\[x_{1} \left[\begin{array}{c} 1 \\ 0 \\ 2 \\ 7 \end{array}\right] + x_{2} \left[\begin{array}{c} 2 \\ 0 \\ 4 \\ 14 \end{array}\right] + x_{3} \left[\begin{array}{c} 2 \\ 1 \\ 3 \\ 14 \end{array}\right] = \left[\begin{array}{c} -4 \\ -1 \\ -7 \\ -28 \end{array}\right]\]</span></p></div>
<ol>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain and demonstrate how to find a simpler linear system that has the same solution set. </p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain whether this solution set has no solutions, one solution, or infinitely-many solutions. If the set is finite, describe it using set notation. </p></div>
</div></li>
</ol>
</div></li>
<li><div class="stx-knowl">
<div class="stx-intro"><p><span class="math display-math" data-latex="x_{1} \left[\begin{array}{c} 0 \\ -1 \\ 0 \\ -2 \end{array}\right] + x_{2} \left[\begin{array}{c} 1 \\ 1 \\ 0 \\ 5 \end{array}\right] + x_{3} \left[\begin{array}{c} 4 \\ 1 \\ 1 \\ 16 \end{array}\right] = \left[\begin{array}{c} -2 \\ 3 \\ -1 \\ -2 \end{array}\right]">\[x_{1} \left[\begin{array}{c} 0 \\ -1 \\ 0 \\ -2 \end{array}\right] + x_{2} \left[\begin{array}{c} 1 \\ 1 \\ 0 \\ 5 \end{array}\right] + x_{3} \left[\begin{array}{c} 4 \\ 1 \\ 1 \\ 16 \end{array}\right] = \left[\begin{array}{c} -2 \\ 3 \\ -1 \\ -2 \end{array}\right]\]</span></p></div>
<ol>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain and demonstrate how to find a simpler linear system that has the same solution set. </p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-content"><p> Explain whether this solution set has no solutions, one solution, or infinitely-many solutions. If the set is finite, describe it using set notation. </p></div>
</div></li>
</ol>
</div></li>
</ol>
</div></div></text>
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<generalfeedback format="html"> <!-- solution text-->
<text><div class="stx"><div class="stx-knowl">
<ol>
<li><div class="stx-knowl">
<ol>
<li><div class="stx-knowl">
<div class="stx-outtro"><p><span class="math display-math" data-latex="\begin{matrix} x_{1} &amp; - &amp; 3 \, x_{2} &amp; &amp; &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}">\[\begin{matrix} x_{1} &amp; - &amp; 3 \, x_{2} &amp; &amp; &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}\]</span></p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-outtro"><p> The solution set has no solutions. The solution set is <span class="math inline-math" data-latex="\emptyset">\(\emptyset\)</span>. </p></div>
</div></li>
</ol>
</div></li>
<li><div class="stx-knowl">
<ol>
<li><div class="stx-knowl">
<div class="stx-outtro"><p><span class="math display-math" data-latex="\begin{matrix} x_{1} &amp; + &amp; 2 \, x_{2} &amp; &amp; &amp; = &amp; -2 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; -1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}">\[\begin{matrix} x_{1} &amp; + &amp; 2 \, x_{2} &amp; &amp; &amp; = &amp; -2 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; -1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}\]</span></p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-outtro"><p> The solution set has infinitely-many solutions. </p></div>
</div></li>
</ol>
</div></li>
<li><div class="stx-knowl">
<ol>
<li><div class="stx-knowl">
<div class="stx-outtro"><p><span class="math display-math" data-latex="\begin{matrix} x_{1} &amp; &amp; &amp; &amp; &amp; = &amp; -2 \\ &amp; &amp; x_{2} &amp; &amp; &amp; = &amp; 2 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; -1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}">\[\begin{matrix} x_{1} &amp; &amp; &amp; &amp; &amp; = &amp; -2 \\ &amp; &amp; x_{2} &amp; &amp; &amp; = &amp; 2 \\ &amp; &amp; &amp; &amp; x_{3} &amp; = &amp; -1 \\ &amp; &amp; &amp; &amp; 0 &amp; = &amp; 0 \\ \end{matrix}\]</span></p></div>
</div></li>
<li><div class="stx-knowl">
<div class="stx-outtro"><p> The solution set has one solution. The solution set is <span class="math inline-math" data-latex="\left\{ \left[\begin{array}{c} -2 \\ 2 \\ -1 \end{array}\right] \right\}">\(\left\{ \left[\begin{array}{c} -2 \\ 2 \\ -1 \end{array}\right] \right\}\)</span>. </p></div>
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</ol>
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</ol>
</div></div></text>
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