chap8-summary.xml

<?xml version="1.0" encoding="UTF-8" ?>
<!-- <mathbook><book> -->

<section xml:id="chap8-summary" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Chapter Summary and Review</title>
<subsection><title>Key Concepts</title>
<p>
	<ol label="1">
		<li><p>We can solve a <m>2\times 2</m> linear system by graphing. The solution is the intersection point of the two graphs.</p></li>
		<li><p>A linear system may be <term>inconsistent</term> (has no solution), <term>dependent</term> (has infinitely many solutions), or <term>consistent and independent</term> (has one solution).</p></li>
		<li><p>
			<xref ref="assemblage-inconsistent-and-dependent"><term>Inconsistent and Dependent Systems</term></xref>
		</p></li>
		<li><p>We can use a system of equations to solve problems involving two unknown quantities.</p></li>
		<li><p>In economics, the price at which the <term>supply</term> and <term>demand</term> are equal is called the <term>equilibrium price</term>.</p></li>
		<li><p>The solution to a <m>3\times 3</m> linear system is an <term>ordered triple</term>.</p></li>
		<li><p>A <m>3\times 3</m> system in <term>triangular form</term> can be solved by <term>back-substitution</term>.</p></li>
		<li><p><term>Gaussian reduction</term> is a generalized form of the elimination method that can be used to reduce a <m>3\times 3</m> linear system to triangular form.</p></li>
		<li><p><xref ref="assemblage-steps-for-solving-3-by-3">Steps for Solving a <m>3\times 3</m> Linear System</xref></p></li>
		<li><p><m>3\times 3</m> linear systems may be <term>inconsistent</term> or <term>dependent</term>.</p></li>
		<li><p>We can use a <term>matrix</term> to represent a system of linear equations. Each row of the matrix consists of the coefficients in one of the equations of the system.</p></li>
		<li><p>We operate on a matrix by using the elementary row operations.</p><p><xref ref="assemblage-elementary-row-operations">Elementary Row Operations</xref></p></li>
		<li><p>We can solve a linear system by matrix reduction.</p><p><xref ref="assemblage-solving-system-by-matrix-reduction">Solving a Linear System by Matrix Reduction</xref></p></li>
		<li><p>
			<xref ref="assemblage-strategy-for-matrix-reduction">Strategy for Matrix Reduction</xref>
		</p></li>
		<li><p>To reduce larger matrices, we start with the first row and work our way along the diagonal, using row operations to obtain nonzero entries on the diagonal and zeros below the diagonal entry.</p></li>
		<li><p>The solutions of a linear inequality in two variables consist of a half-plane on one side of the line. The line itself is not included if the inequality is strict.</p></li>
		<li><p>Once we have graphed the boundary line, we can decide which half-plane to shade by using a <term>test point</term>.</p></li>
		<li><p><xref ref="assemblage-graph-inequality-using-test-point">To Graph an Inequality Using a Test Point:</xref></p></li>
		<li><p>The solutions to a system of inequalities include all points that are solutions to each inequality in the system. The graph of the system is the intersection of the shaded regions for each inequality in the system</p></li>
		<li><p>To describe the solutions of a system of inequalities, it is useful to locate the <term>vertices</term>, or corner points, of the boundary.</p></li>
		<li><p><term>Linear programming</term> is a technique for finding the maximum or minimum value of an <term>objective function</term>, subject to a system of <term>constraints</term>.</p></li>
		<li><p>The optimum solution occurs at one of the vertices of the set of <term>feasible solutions</term>.</p></li>
		<li><p><xref ref="assemblage-solve-linear-programming-problem">To Solve a Linear Programming Problem</xref></p></li>
	</ol>.
</p>
</subsection>
<!-- <subsubsection> -->
	<xi:include href="./chap8-rev-problems.xml" />   <!-- exercises  -->
<!-- </subsubsection> -->

</section>
<!-- </appendix> -->
<!-- </book>  </mathbook> -->