By Murray Bourne, 07 Feb 2011
A lot of students get mixed up when trying to multiply 2 matrices.
They either cannot follow the procedure, or get lost with the mental multiplication and addition steps (or lose track of what they are doing in their calculator).
Considering there are 27 multiplications and 18 additions (45 operations in all) for a basic 3×3 times 3×3 matrix multiplication, it's probably not that surprising.
I wrote an interactive applet that demonstrates matrix multiplication with animations. It allows the user to choose different matrix sizes and then see how they are added, subtracted or multiplied (including by a scalar). Different random numbers are used for each example.
You can find the applet here: Add, Subtract and Multiply matrices interactive.
Here's a matrix multiplication explanation page. You can choose a few different sized matrices to get an idea what happens in those cases.
You can find it here: Multiplying matrices - examples.
The script is PHP and the output uses tables, not images. This gives the quickest and cleanest output for mobile devices.
Of course (and I can't help myself here), it would be better to get students to use a computer to multiply matrices, rather than churn their way through hundreds of calculation steps, and still have no idea why. My explanation page still has a place though - we still need to know the concept of matrix multiplication!
Any suggestions or comments?
See the 2 Comments below.