Linear Algebra I: Course Notes for Math 2050
Edition: 2
Copyright: 2016
Pages: 236
Edition: 2
Copyright: 2016
Pages: 236
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Linear Algebra I: Course Notes for Math 2050 is a comprehensive textbook designed for an introductory college-level course in linear algebra. The text presents the fundamental concepts of vector spaces, matrices, systems of linear equations, determinants, and eigenvalues through a structured, week-by-week format that emphasizes both mathematical theory and practical problem-solving. Students develop a strong foundation in linear algebra by exploring vector operations, geometric interpretations, matrix algebra, Gaussian elimination, matrix factorizations, and the relationships between linear transformations and systems of equations.
In addition to core concepts, the course notes introduce important applications of linear algebra, including electric circuits and matrix-based coding systems, helping students connect abstract mathematics to real-world problems. Practice exercises, review materials, true/false questions, self-assessment activities, and a comprehensive glossary reinforce learning throughout the course. This text serves as an effective resource for students in mathematics, engineering, computer science, physics, and other STEM disciplines seeking a solid understanding of linear algebra and its applications.
To My Students
To My Colleagues
Unit 1: Euclidean n-Space
Week 1
Vectors
Higher Dimensions
Linear Combinations
The Span of Vectors
The Standard Basis Vectors
Week 2
The Length of a Vector
Dot Product and Angle Between Vectors
Some Inequalities
Week 3
The Equation of a Plane
The Cross Product
The Equation of a Line
Week 4
Projections
The Distance from a Point to a Plane
The Distance from a Point to a Line
Linear Independence and Dependence
Unit 2: Matrices and Linear Equations
Week 5
Matrices
Matrix Algebra
The Significance of Ax
Week 6
Systems of Linear Equations
Gaussian Elimination
Row Echelon Form
Week 7
Homogeneous Systems
The Inverse of a Matrix
Matrix Equations
Finding the Inverse of a Matrix
Week 8
Elementary Matrices
LU Factorization
PLU Factorization
Unit 3: Determinants
Week 9
Minors and Cofactors
Computing Determinants
Week 10
Properties of Determinants
Using Elementary Row Operations to Find Determinants
Unit 4: The Equation Ax = λx
Weeks 11 and 12
Complex Numbers
Eigenvalues and Eigenvectors
Similarity and Diagonalization
Appendix: Applications
Electric Circuits
Using Matrices to Generate Codes
Additional Resources
Suggested Homework Exercises
Answers to True/False Questions
Solutions to Test Yourself Exercises
Things I Must Remember
Glossary
Index
B.Sc. in Mathematics, University of Toronto (1969)
Ph.D. in Mathematics, University of British Columbia (1973)
Edgar G. Goodaire is a Canadian mathematician and author, best known for his work in nonassociative algebra, particularly in the study of loops such as Moufang and Bol loops, and alternative rings. He is also recognized for his contributions to discrete mathematics and linear algebra in teaching and curriculum development.