xvi Contents 11.2 Systems of Linear Equations: Matrices 769 Write the Augmented Matrix of a System of Linear Equations • Write the System of Equations from the Augmented Matrix • Perform Row Operations on a Matrix • Solve a System of Linear Equations Using Matrices 11.3 Systems of Linear Equations: Determinants 784 Evaluate 2 by 2 Determinants • Use Cramer’s Rule to Solve a System of Two Equations Containing Two Variables • Evaluate 3 by 3 Determinants • Use Cramer’s Rule to Solve a System of Three Equations Containing Three Variables • Know Properties of Determinants 11.4 Matrix Algebra 795 Find the Sum and Difference of Two Matrices • Find Scalar Multiples of a Matrix • Find the Product of Two Matrices • Find the Inverse of a Matrix • Solve a System of Linear Equations Using an Inverse Matrix 11.5 Partial Fraction Decomposition 812 Decompose P Q where Q Has Only Nonrepeated Linear Factors • Decompose P Q where Q Has Repeated Linear Factors • Decompose P Q where Q Has a Nonrepeated Irreducible Quadratic Factor • Decompose P Q where Q Has a Repeated Irreducible Quadratic Factor 11.6 Systems of Nonlinear Equations 821 Solve a System of Nonlinear Equations Using Substitution • Solve a System of Nonlinear Equations Using Elimination 11.7 Systems of Inequalities 831 Graph an Inequality by Hand • Graph an Inequality Using a Graphing Utility • Graph a System of Inequalities 11.8 Linear Programming 840 Set Up a Linear Programming Problem • Solve a Linear Programming Problem Chapter Review 847 Chapter Test 851 Cumulative Review 852 Chapter Project 853 12 Sequences; Induction; the Binomial Theorem 854 12.1 Sequences 855 List the First Several Terms of a Sequence • List the Terms of a Sequence Defined by a Recursive Formula • Use Summation Notation • Find the Sum of a Sequence Algebraically and Using a Graphing Utility • Solve Annuity and Amortization Problems Using Recursive Formulas 12.2 Arithmetic Sequences 869 Determine Whether a Sequence Is Arithmetic • Find a Formula for an Arithmetic Sequence • Find the Sum of an Arithmetic Sequence 12.3 Geometric Sequences; Geometric Series 875 Determine Whether a Sequence Is Geometric • Find a Formula for a Geometric Sequence • Find the Sum of a Geometric Sequence • Determine Whether a Geometric Series Converges or Diverges • Solve Annuity Problems Using Formulas 12.4 The Limit of a Sequence; Infinite Series 887 Find the Limit of a Sequence • Define Infinite Series and Geometric Series 12.5 Mathematical Induction 894 Prove Statements Using Mathematical Induction
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