This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]
This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]
This 18-minute video lesson shows how to solve a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 30 of 143]
This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]
This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]
This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]
This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]
This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]
This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.
This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.
This 23-minute video lesson looks at Rowspace and Left Nullspace. [Linear Algebra playlist: Lesson 97 of 143]
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however.
This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.
The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
This 9-minute video lesson provides definitions of the vector dot product and vector length.
This 19-minute video lesson proves the triangle inequality for vectors in Rn.
This 20-minute video lesson looks at the relationship between left nullspace, rowspace, column space and nullspace. [Linear Algebra playlist: Lesson 98 of 143]
After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today’s students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning.
Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work.
The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
An adaptation for MAT223 UTM
Short Description:
This open textbook is an adaptation of Linear Algebra with Applications by W. Keith Nicholson. The original book can be found and downloaded from Lyryx.com. Five topics are covered here: system of linear equations, matrix algebra, determinants and diagonalization, vector geometry and vector space. It's suitable for beginners who are interested in learning linear algebra. Readers will have the opportunity to work through H5P elements embedded in every chapter to check their understanding of core concepts on their own.
Word Count: 53792
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
This Open Middle task asks students to create a table of values that represents a linear function.
This activity is a culmnating assessment of students' abilities to describe a linear function in words, in an equation, in a table, in a graph, identify a solution, and explain the solution.