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 1