Chapter 1 Matrices 1.1 Basic Concepts of Matrix 1.1.1 Definition of Matrix 1.1.2 Special Matrices 1.1.3 Application Examples 1.2 Oraios of Matrices 1.2.1 Linear oraios of matrices 1.2.2 Multiplication of Matrices 1.. Transpose of a Matrix 1.2.4 Application Examples 1.3 Matrix Inverses 1.3.1 Invertible Matrices 1.3.2 Orthogonal Matrices 1.4 Blocks of Matrices 1.4.1 Block Oraios 1.4.2 Block diagonal matrices 1.5 Elementary Oraios and Gauss-Jordan Elimination 1.5.1 Elementary Oraios 1.5.2 Gauss-Jordan Elimination 1.6 Elementary Matrices and a Method for Finding A-1 1.6.1 Elementary Matrices 1.6.2 A Method for Finding A-1 MATLAB EXERCISES Chapter 2 Determinants 2.1 Introduction to Determinants 2.1.1 Definitions of Determinants 2.1.2 On the Row(Column) Expansion 2.2 Properties and Evaluation of Determinants 2.2.1 Properties 2.2.2 Evaluation . Applications of Determinants ..1 Adjugate Matrices and Inverse Formula ..2 Cramer' s rule .. Application Examples MATLAB EXERCISES Chapter 3 Vector Spaces and Linear Systems 3.1 Linear Dependence and Independence 3.2 Vector Spaces 3.2.1 Definition and Examples 3.2.2 Subspaces 3.. The span of a set of vectors 3.3 Basis and Dimension 3.4 Rank 3.5 Structure for Linear Systems Solution Set 3.5.1 Homogeneous Systems 3.5.2 Non-Homogeneous Systems MATLAB EXERCISES Chapter 4 Eigenvalues and Eigenvectors 4.1 The Concepts of Eigenvalues and Eigenvectors 4.2 Diagonalization