Mathematical Methods

Contents

About the Author

Preface

1 Matrices and Linear Systems of Equations

1.1 Introduction

1.2 Algebra of Matrices

1.3 Matrix Multiplication

1.4 Determinant of a Square Matrix

1.5 Related Matrices

1.6 Determinant-Related Matrices

1.7 Special Matrices

Exercise 1.1

1.8 Linear Systems of Equations

1.9 Homogeneous (H) and Nonhomogeneous (NH) Systems of Equations

1.10 Elementary Row and Column Operations (Transformations) for Matrices

Exercise 1.2

1.11 Inversion of a Nonsingular Matrix

Exercise 1.3

1.12 Rank of a Matrix

1.13 Methods for Finding the Rank of a Matrix

Exercise 1.4

1.14 Existence and Uniqueness of Solutions of a System of Linear Equations

1.15 Methods of Solution of NH and H Equations

1.16 Homogeneous System of Equations (H)

Exercise ...