This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.
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 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).
This task requires students to use the fact that on the graph of the linear function h(x)=ax+b, the y-coordinate increases by a when x increases by one. Specific values for a and b were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.
Students use latex tubes and bicycle pumps to conduct experiments to gather data about the relationship between latex strength and air pressure. Then they use this data to extrapolate latex strength to the size of latex tubing that would be needed in modern passenger sedans to serve as hybrid vehicle accelerators, thus answering the engineering design challenge question posed in the first lesson of this unit. Students input data into Excel spreadsheets and generate best fit lines by the selection of two data points from their experimental research data. They discuss the y-intercept and slope as it pertains to the mathematical model they generated. Students use the slope of the line to interpret the data collected. Then they extrapolate with this information to predict the latex dimensions that would be required for a full-size hydraulic accumulator installed in a passenger vehicle.