Math 4A
Linear Algebra with Applications
Video - 9:59 | Introduction to row reduction | Continued in part 2 |
Video - 7:12 | Example of solving a linear system (unique solution) |
Video - 17:43 | Solves a linear system that has an infinite solution set | See following 2 videos for more examples |
Text | Description and examples of matrix (elementary) row operations |
Interactive | Allows you to enter in a matrix and then select which row operations you wish to perform | Good way to check whether your work for arithmetic errors |
Interactive | Allows you to enter in a matrix and then shows step-by-step which row operations are used to put matrix into RREF |
Interactive | Allows you to enter in an augmented matrix and then shows step-by-step which row operations are used to solve the system of equations |
Video - 16:31 | Lecture on vectors |
Interactive | Exercises on vectors |
Video - 4:46 | Introduction to vectors and magnitude |
Video - 20:34 | Lecture on span |
Interactive | Do-it-all mathematics tool | Use Span (Ex: Span{(1,2),(3,4)}) to calculate the span of an entered set of vectors |
Interactive | Allows you to enter in a set of vectors of R^n, P^n, or M^n, and shows how to determine whether the set spans the space |
Video - 17:06 | Examples of finding the span of a set of vectors |
Video - 15:46 | Lecture on linear independence | See following two videos for more formal definition and examples |
Interactive | Do-it-all mathematics tool | Use Linear Independence (Ex: Linear Indepence {(1,2),(3,4)}) to determine whether entered vectors are linearly independent |
Interactive | Allows you to enter in a set of vectors of R^n, P^n, or M^n, and shows how to determine linear independence |
Video - 8:05 | Examples on determining whether a set of vectors is linearly independent |
Video - 13:52 | Lecture on linear transformations |
Video - 17:32 | Determining the matrix of a linear transformation given how it acts on basis vectors |
Interactive | Visualize how a linear transformation corresponding to a 2x2 matrix affects a pentagon |
Video - 9:06 | Definition of a linear transformation and then some examples |
Video - 18:14 | Example of a matrix product |
Video - 5:25 | Matrix addition, subtraction, scalar multiplication |
Video - 9:38 | Example of a matrix product |
Video - 6:22 | Example of finding a matrix inverse |
Interactive | Do-it-all mathematics tool | Enter in matrix (ex: {{1,2,3},{3,2,1},{2,1,3}}) and will find inverse |
Interactive | Allows you to enter in a square matrix and then will show step-by-step how to find its inverse |
Text | Description and examples for finding the inverse of a matrix |
Video - 10:01 | Example of finding a 3x3 determinant |
Video - 6:56 | How to find a 3x3 determinant |
Interactive | Do-it-all mathematics tool | Enter in matrix (ex: {{1,2,3},{3,2,1},{2,1,3}}) and will calculate its determinant |
Text | Description on taking determinants using cofactor expansion, and by using row operations |
Video - 23:39 | Lecture on subspaces of R^n |
Video - 10:23 | Lecture on the null space of a matrix |
Video - 10:40 | Lecture on the column space of a matrix |
Video - 19:00 | Lecture on bases |
Interactive | Allows you to enter in a set of vectors of R^n, P^n, or M^n, and determines if the set is a basis |
Video - 7:17 | Examples on finding the basis of a set of vectors |
Video - 16:06 | Lecture on coordinate systems |
Video - 12:48 | Lecture on rank |
Video - 7:43 | Lecture on eigenvectors and eigenvalues |
Interactive | Do-it-all mathematics tool | Enter in matrix (ex: {{1,2,3},{3,2,1},{2,1,3}}) and will calculate its eigenvalues/eigenvectors |
Video - | Slides with lecture on characteristic equation and finding eigenvalues |
Video - | Slides with lecture on finding eigenvectors |
Interactive | Interactive applet that calculates eigenvalues/eigenvectors and plots the image of the unit circle under a transformation |
Video - 13:09 | Lecture on diagonalization |
Video - | Slides with lecture on diagonalization |
Video - 17:26 | Lecture on projections |
Video - 11:16 | Lecture on orthonormal bases |
Video - 15:32 | Lecture on least squares approximation | Next two videos give examples |
Text | List and descriptions of applications of linear algebra |
Text | On the increasing popularity of math-based sports rankings |
Text | Background behind Google's PageRank algorithm |
Text | For the adventurous student - a more detailed look at how linear algebra powers Google's PageRank algorithm |