Introduction to matrices, their properties, and basic operations explained in an easy-to-understand manner.

Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

This topic covers: - Adding & subtracting matrices - Multiplying matrices by scalars - Multiplying matrices - Representing & solving linear systems with matrices - Matrix inverses - Matrix determinants - …

Sal defines what it means to add or subtract matrices. He shows a few examples and discusses some important properties of matrix addition and subtraction.

The left half of the matrix should be the identity matrix, and the right half should be the inverse of A. If you can't get [A|I] to reduce to [I|A^-1], then the matrix A is not invertible.

I'm going to not formally define it, but this is just a set of vectors. I mean sometimes we visualize it as multi-dimensional space and all that, but if we wanted to be just as abstract about it as possible, it's …

If you take the composition of one linear transformation with another, the resulting transformation matrix is just the product, as we've just defined it, of their two transformation matrices.

2X2 matrices can define transformations for the entire plane. In this worked example, we see how to find the image of a given vector under the transformation defined by a given matrix.

Learn about the properties of matrix scalar multiplication (like the distributive property) and how they relate to real number multiplication.

A graph represents a single function, from x onto y. A matrix holds a lot more information than that. Matrices perform transformations on the entire space they act upon, so I'm not particularly sure what …