Linear Algebra Problem Solving Guide: Concepts, Methods, and Techniques

Author: Wang Zhongliang
Publisher:
Publishing Date: 2004-09-01
Features: This book is a learning guide for undergraduate students in engineering, economics, management, and finance majors at higher education institutions, covering the fundamental mathematics course "Linear Algebra." The book is divided into six chapters, including topics such as determinants, matrices, systems of linear equations and vectors, vector spaces, eigenvalues and eigenvectors of matrices, and quadratic forms. Each chapter is structured into four parts: content summary, basic requirements and key points, analysis of difficulties, and solved examples of typical problems. It is designed to complement and be used synchronously with domestic unified textbooks. At the end of the book, there are two appendices: Appendix I presents the 2004 postgraduate entrance examination questions on linear algebra, while Appendix II provides answers, hints, and solutions to the exercises in each chapter, as well as solutions to teaching and research examination questions from 2004. This book is written in accordance with the original Ministry of Education's basic requirements for teaching linear algebra in engineering programs and references the national postgraduate entrance examination "Mathematics Examination Syllabus," combining the authors' extensive experience and insights in teaching and tutoring linear algebra. The key part of the book is the "Solved Examples" section, which includes 300 examples categorized by type, such as fill-in-the-blank questions, multiple-choice questions, problem-solving questions, and proof questions. Using a "explain the concept, provide examples" and "provide examples, explain methods" approach, it helps readers correctly understand the basic concepts and theories of linear algebra, master common problem-solving methods and techniques, and especially offers multiple solutions to many examples. This enables readers to broaden their thinking, improve their analytical and problem-solving skills, and achieve a comprehensive understanding with the ability to apply knowledge to different situations. This book can serve as a supplementary textbook for undergraduate students in relevant majors studying "Linear Algebra," a teaching reference for instructors, and a valuable study guide for readers preparing for postgraduate entrance examinations.