MT-A315 Introduction to Linear Algebra

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

In this introduction to functions video, Sal gives an intuitive definition of what a function is and introduces the function notion, f(x). He finishes the video by looking at a simple example of evaluating g(f(x)) without getting into...

Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...

What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...

Take a look at vectors as geometric objects and then as an algebraic concept. The second video in a series of 15 introduces the vector using three perspectives: the physics, computer science, and mathematical. The resource shows the...

The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...

It is all about perspective. A video introduces the idea that the view of a vector all depends upon the perspective of the basis vectors. Knowing how to go from one coordinate system's basis vectors to another system's basis vectors...

But what happens if the matrix is not square? The ninth video in a series of 15 serves as a footnote to discuss non-square matrices. The resource presents them as transformations between two and three dimensions. The presentation...

A linear algebra worksheet where pupils explore three linear equations and use Gaussain elimination to solve the system of equations. They identify values that have no solution, one solution, and many solutions. There is one open-ended,...

In this linear algebra worksheet, students apply the basics of algebraic reasoning to evaluate different expressions looking for the pattern of finding the unknowns.