xiv CONTENTS 9.4 Partial Fractions 920 Decomposition of Rational Expressions ■ Distinct Linear Factors ■ Repeated Linear Factors ■ Distinct Linear and Quadratic Factors ■ Repeated Quadratic Factors Chapter 9 Quiz (Sections 9.1–9.4) 927 9.5 Nonlinear Systems of Equations 928 Nonlinear Systems with Real Solutions ■ Nonlinear Systems with Nonreal Complex Solutions ■ An Application of Nonlinear Systems Summary Exercises on Systems of Equations 938 9.6 Systems of Inequalities and Linear Programming 939 Linear Inequalities in Two Variables ■ Nonlinear Inequalities in Two Variables ■ Systems of Inequalities ■ Linear Programming 9.7 Properties of Matrices 951 Basic Definitions ■ Matrix Addition ■ Special Matrices ■ Matrix Subtraction ■ Scalar Multiplication ■ Matrix Multiplication ■ An Application of Matrix Algebra 9.8 Matrix Inverses 965 Identity Matrices ■ Multiplicative Inverses ■ Solution of Systems Using Inverse Matrices Test Prep 977 ■ Review Exercises 982 ■ Test 988 11 Further Topics in Algebra 1039 11.1 Sequences and Series 1040 Sequences ■ Series and Summation Notation ■ Summation Properties and Rules 10 Analytic Geometry 991 10.1 Parabolas 992 Conic Sections ■ Horizontal Parabolas ■ Geometric Definition and Equations of Parabolas ■ An Application of Parabolas 10.2 Ellipses 1001 Equations and Graphs of Ellipses ■ Translated Ellipses ■ Eccentricity ■ Applications of Ellipses Chapter 10 Quiz (Sections 10.1–10.2) 1014 10.3 Hyperbolas 1014 Equations and Graphs of Hyperbolas ■ Translated Hyperbolas ■ Eccentricity 10.4 Summary of the Conic Sections 1025 Characteristics ■ Identifying Conic Sections ■ Geometric Definition of Conic Sections Test Prep 1032 ■ Review Exercises 1034 ■ Test 1037
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