Chapter 1 Equation Systems and Matrices 1.1 Systems of Linear Equations 1.1.1 Brief History o Aebra and Linear Algebra 1.1.2 Systems of Linear Equations 1.1.3 Strict Triangular Form of Linear Systems 1.2 Linear System in Matrix 1.2.1 Matrix Notations 1.2.2 Solving Linear Systems 1.3 Reduced Row Echelon Form 1.3.1 Row Echelon Form 1.3.2 Gauss Elimination 1.3.3 Reduced Row Echelon 1.4 Consistency of Linear Systems 1.4.1 Overdetermined Systems 1.4.2 Underdetermined Systems 1.4.3 Homogeneous Systems Chapter 2 Matrix Algebra 2.1 Notations and Oraios 2.1.1 Matrix Notations 2.1.2 Matrix Oraios 2.1.3 Algebraic Rules of Matrix Oraios 2.2 Inverse and Transpose of Matrices 2.2.1 Identity Matrix 2.2.2 Matrix Inverse 2.. The Transpose of a Matrix 2.2.4 Triangular and Diagonal Matrices . Partitioned Matrices ..1 The Notations of Partitioned Matrices ..2 Block Addition and Scalar Multiplication .. Block Multiplication 2.4 Linear Combination of Vectors 2.4.1 Linear Combination of Vectors 2.4.2 Equivalent Systems 2.4.3 Elementary Matrices 2.4.4 Find the Inverse Matrix 2.5 The Determinant of a Matrix 2.5.1 CASE I The Determinant of 1 x 1 Matrices 2.5.2 CASE II The Determinant of 2 x 2 Matrices 2.5.3 CASE III 3 x 3 Matrices 2.5.4 CASE IV The Determinant of n x n Matrices 2.6 Properties of Determinants 2.6.1 Determinant of the Transposed Matrix 2.6.2 Determinant of Triangular Matrices 2.6.3 Determinant of Matrices with All Zeros in a Row or Column" 2.6.4 Determinant of Matrices with Identical Rows or Columns 2.6.5 *Laplace's Definition of Determinant by Using Subdeterminant 2.6.6 Algebraic Rules of Determinants 2.6.7 Determinant and Singularity of a Matrix 2.7 Cramer's Rule 2.7.1 The Adjoint of a Matrix