Chapter 1 Vector Spaces 1.1 Introduction 1.2 The geometry and algebra of vectors 1.3 Operations of vectors and their applications 1.4 Lines and planes in 3-dimensional space 1.5 Review exercises Chapter 2 Systems of Linear Equations 2.1 Introduction 2.2 Solutions of linear systems: elimination method 2.3 Structure of solutions of linear systems and linear independence 2.4 Subspaces of and linear transformation 2.5 Applications 2.6 Review exercises Chapter 3 Matrix Algebra 3.1 Introduction 3.2 Definitions and basic operations of matrices 3.3 Matrix multiplication 3.4 The inverse of a matrix 3.5 Elementary matrices 3.6 Review exercises Chapter 4 Determinants 4.1 Introduction 4.2 The definition and properties of determinants 4.3 Geometric interpretations of determinants 4.4 Applications of determinants 4.5 Review exercises Chapter 5 Eigenvalues and Eigenvectors 5.1 Introduction 5.2 Definitions of eigenvalues and eigenvectors 5.3 Properties of eigenvalues and eigenvectors 5.4 Eigenvalues and eigenvectors of symmetric matrices 5.5 Similarity and diagonalization 5.6 Quadratic forms 5.7 Applications 5.8 Review exercises Answers to Exercises Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 References Index of Vocabulary Index of Notation
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