In this series of five videos, you will learn how to solve systems of linear equations with any number of variables, using a process involving matrices. The process is often called row reduction, or more specifically, Gauss-Jordan elimination. If you like, you can view a PDF version of the slides.
- The first video will introduce you to matrices and give you a bird’s-eye view of the three stages of row reduction.
- The second video will introduce you to the so-called row operations that are used in row reduction.
- In the third video, you will learn what it means for a matrix to be reduced (in other words, to be in what is called reduced row echelon form). Knowing this will help you understand the goal of row reduction and when you should use certain row operations. At the end of the next video, you’ll be ready to learn a quicker way to decide if a matrix is reduced.
- In the fourth video, we will solve our first system and learn guidelines that will help us to know what to do at each step. At the end of the video, we discuss a quick way to decide when a matrix is reduced (in other words, when a matrix is in reduced row echelon form).
- In the fifth video, we will learn how many solutions a system of linear equations can have (no solution, a unique solution, or infinitely many solutions), and we’ll learn how to deal with each case.