Khan Academy: Changing Coordinate Systems to Help Find a Transformation Matrix

Video showing how to change coordinate systems to make finding the transformation matrix with respect to the standard basis easier. First, a specific linear transformation is defined and the regular method for constructing the...

Video defining eigenvectors as scaled vectors and eigenvalues as their scale value and explaining their significance. Video references the example from a previous video about changing coordinate systems to make finding the transformation...

This video demonstrates how to solve a system of linear equations by substitution. It also takes it a step further and graphs the system of equations on a coordinate grid. [6:04]

This video demonstrates how to solve a system of linear equations by graphing and finding the point of intersection. [6:35]

This video demonstrates how to solve and graph a given system of equations by eliminating a variable. [4:58]

In this video lesson students learn to solve systems of equations by the graphing method. After graphing, students then determine the number of solutions the system has by looking at the intersection of the lines.

Sal explains what it means to simplify a rational expression and why we would want to do that. Just don't forget the excluded values! [15:22]

Example of finding the transformation matrix for an alternate basis.

Video explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]

This video demonstrates how to set up and solve a system of equations in order to solve a word problem. The system is solved using the elimination method. [5:51]