Matrix Multiplication and Solving Systems of Equations

Last week we talked about the basic operations of matrices and how to find a matrix inverse. This week we will continue to our discussion of matrices by talking about matrix multiplication and solving systems of equations using matrices.

I recommend starting the discussion by talking about when matrix multiplication can occur. Remember that if two matrices can be multiplied, their inner dimensions are the same. For example, if matrix A has dimensions 2 x 4 and matrix B has dimensions 4 x 5 then the matrices can be multiplied since the inner dimensions of 4 are the same. The product matrix will have dimensions 2 x 5. It is important to start with this fact so that students do not spend time working on problems that can’t be completed.

The following are some helpful websites that I found that can help students and teachers work through the concept of matrix multiplication.

The Math Warehouse website has a great step by step explanation of matrix multiplication. There are great tutorials as well that take students through the entire process.

Most graphing calculators will do matrix multiplication for students but we can’t expect all students to be able to own or use a graphing calculator. There are some great online calculators such as the Easy Calculations Calculator and the Analyze Math Applet. Students can use these sites to check their work.

Solving systems of equations is also a concept that utilizes matrices, especially when working with three equations and three unknowns. Matrices are the easiest way to solve these types of problems. Spark Notes and Cliff Notes both have great summaries of how matrices can be used to solve systems of equations. I also found a great tutorial on how to use graphing calculators to solve systems of equations using matrices.

As always, please share your finds with the rest of the readers. Next week we will talk more closely about proofs.