The Matrix Algebra Tutor

In this lesson, the student will learn what a matrix is in algebra and how to perform basic operations on matrices. We will learn how to do basic matrix math operations by solving example problems.

Now that the student understands what a matrix is, this section focuses on teaching how to add and subtract matrices. In addition, the student is taught how to properly multiply a matrix by a scalar (a number)....

This section focuses on teaching the central topic of multiplying two matrices together. Many students find this topic difficult, but by viewing the numerous examples in this section, this topic is easily understood....

In this section, the student will learn how to manipulate the rows of a matrix to make the matrix simpler. These techniques are used throughout the remainder of the course and are very important to master. Numerous worked examples illustrate the technique....

In this section, learn how to represent a system of algebraic equations as a matrix. We learn how to manipulate the rows of the matrix according to the Gaussian and Gauss-Jordan methods in order to arrive at the solution....

In this section, we learn how to identify if a system of algebraic equations is inconsistent or dependent. This information is used in order to arrive at the solution to the problem....

This section focuses on explaining the concept of the inverse of a matrix. Numerous examples are worked to show the student how to calculate a matrix inverse and what it is used for....

We now turn our attention to the topic of using the matrix inverse in order to solve a system of equations. Numerous problems are worked that show the student how to use the inverse correctly in order to solve the system....

In this video tutorial, the concept of a matrix determinant is introduced. The determinant is an important quantity to know how to calculate, and many examples are worked to demonstrate the procedure....

Cramer's rule is a powerful technique that uses the matrix determinant in order to solve a system of equations. Numerous examples are worked in order to demonstrate the technique....