ContentsChapter 1 Vector Spaces 11.1 Introduction 11.2 The geometry and algebra of vectors 11.3 Operations of vectors and their applications 121.4 Lines and planes in 3-dimensional space 281.5 Review exercises 35Chapter 2 Systems of Linear Equations 382.1 Introduction 382.2 Solutions of linear systems: elimination method 402.3 Structure of solutions of linear systems and linear independence 512.4 Subspaces of and linear transformation 632.5 Applications 692.6 Review exercises 80Chapter 3 Matrix Algebra 853.1 Introduction 853.2 Definitions and basic operations of matrices 863.3 Matrix multiplication 913.4 The inverse of a matrix 1033.5 Elementary matrices 1113.6 Review exercises 116Chapter 4 Determinants 1204.1 Introduction 1204.2 The definition and properties of determinants 1214.3 Geometric interpretations of determinants 1304.4 Applications of determinants 1334.5 Review exercises 141Chapter 5 Eigenvalues and Eigenvectors 1455.1 Introduction 1455.2 Definitions of eigenvalues and eigenvectors 1465.3 Properties of eigenvalues and eigenvectors 1555.4 Eigenvalues and eigenvectors of symmetric matrices 1605.5 Similarity and diagonalization 1695.6 Quadratic forms 1775.7 Applications 1855.8 Review exercises 188Answers to Exercises 192Chapter 1 192Chapter 2 197Chapter 3 205Chapter 4 213Chapter 5 217References 229Index of Vocabulary 230Index of Notation 233
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