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Download Chapter 3 - Solving Systems of Linear Equations (11.6 MB)

Download Chapter 4 - A Sampling of Linear Models (17.2 MB)

Download Interlude - Abstract Linear Transformations and Vector Spaces (845 KB)

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This book develops linear algebra around matrices. Vector spaces in the abstract are not considered, only vector spaces associated with matrices. This book puts problem solving and an intuitive treatment of theory first, with a proof-oriented approach intended to come in a second course, the same way that calculus is taught. The book's organization is straightforward: Chapter 1 has introductory linear models; Chapter 2 has the basics of matrix algebra; Chapter 3 develops different ways to solve a system of equations; Chapter 4 has applications, and Chapter 5 has vector-space theory associated with matrices and related topics such as pseudoinverses and orthogonalization. Many linear algebra textbooks start immediately with Gaussian elimination, before any matrix algebra. Here we first pose problems in Chapter 1, then develop a mathematical language for representing and recasting the problems in Chapter 2, and then look at ways to solve the problems in Chapter 3-four different solution methods are presented with an analysis of strengths and weaknesses of each.

Publication Date



Basix Custom Publishing


Stony Brook


linear algebra, Markov chains, linear programming, economic input-output models, regression


Algebra | Mathematics


The first people to thank for help with this book are relatives. My father, A. W. Tucker, ignited and nurtured my born-again interest in linear algebra. Notes from the linear algebra course of my brother, Tom Tucker at Colgate, formed the foundation of early work on this book. My family- wife, Mandy, and daughters, Lisa and Katie-provided a supportive atmosphere that eased the long hours of writing; more concretely, Lisa's calculus project on cubic splines became the appendix to Section 4. 7. Preface After the first draft was finished and initial reviews indicated that much • rewriting was needed, the book might have died had not Don Small offered 10 help with the revision work. He added new examples, reworked several sections, and generally made the text better. Many people have read various versions of this book and offered helpful suggestions, including Don Albers, Richard Alo, Tony Ralston, and Margaret Wright. Brian Kohn, Tom Hagstrom, and Roger Lutzenheiser class-tested preliminary versions of this book.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Introduction to Linear Algebra: Models, Methods, and Theory

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Algebra Commons



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