Chapter 1 Systems of Linear Equations and Elementary Operations on Matrices 1．1 Systems of Linear Equations 1．1．1 Definition 1．1．2 Equivalent Systems and Gaussian Elimination Method Exercises 1．1 1．2 Elementary Operations on Matrices 1．2．1 Elementary Row Operations 1．2．2 Row Echelon Forms 1．2．3 Standard Form of a Matrix Exercises 1．2 Chapter 2 Determinants 2．1 The Determinant of a Matrix 2．1．1 Determinants of order 2 and order 3 2．1．2 Permutations and Number of Inversions 2．1．3 Determinant of an nXn Matrix Exercises2．1 2．2 Properties of Determinants Exercises2．2 2．3 The Cofactor Expansion of a Determinant Exercises2．3 2．4 Cramer's Rule Exercises 2．4 Chapter 3 Matrices Algebra 3．1 Matrices Arithmetic 3．1．1Matrices 3．1．2Matrix Addition 3．1．3 Scalar Multiplication 3．1．4 Matrix Multiplication 3．1．5 Powcrs of a Square Matrix Exercise 3．1 3．2Special Matrices 3．2．1The Identity Matrix 3．2．2 The DiagonalMatrix 3．2．3 Triangular Matrices 3．2．4 The Transpose of a Matrix 3．2．5 Symmetric and Skew-Symmetric Matriccs 3．2．6The Determinant of the Product AB 3．2．7 Adjoint ofa Matrix Exercises 3．2 3．3 The Inverse of a Mtrix 3．3．1 Thelnverse of a Matrix 3．3．2Properties of Invertible Matrices Exercises 3．3 3．4 Partitioned Matrices 3．4．1 Partitioned Matrices 3．4．2Operations on Partitioned Matrices Exercises 3．4 3．5 Elementary Matrices 3．5．1 Elementary Matrices 3．5．2Theorems of Invertible Matrices 3．5．3 Computing the Inverse by Elementary Row Operations 3．5．4 Solving Matrix Equations by Elementary Row Operations Exercises 3．5 3．6 The Rank of a Matrix 3．6．1 The Rank of a Matrix 3．6．2 Properties of the Ranks of Matrices Exercises 3．6 Chapter 4 Structure of Solutions for Systems of Linear Equations Chapter 5 Similar Matrices and Quadratic Forms Answers to Exercises References
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