I am always looking for better ways to teach matrices and while researching the topic, I found a new article in the International Journal of Information and Education Technology which focuses on using spread sheets to teach matrices.
Since this is more of an academic paper, it contains a lot more background information than most suggestions. The focus of this specific paper is to show how students can use MS Excel to manipulate matrix.
Although this is a 6 page article, it has tons of pictures with directions so it is easy to follow. In addition, the article also looks at solving three systems of equations using matrices. I like the idea of using the spread sheet to teach math when I can.
If you don't have access to the standard spreadsheets, you can always use Geogebra. Geogebra provides a great tutorial with step by step instructions for using their spreadsheet product. The instructions are for a 2 by 2 matrix but they are very clear. In addition, there are directions showing how to create a visual vector display of the matrix. I like this because it takes students step by step through the process before they are assigned their first problem.
I also found this article that has some great visual drawings to show matrices in a better way than the usual one used in textbooks. It is also written in plain English and easy to understand for people who are not the usual math or science geek. However, it is the visual representation I really like because some people need the visualization to understand what is happening. In addition, it goes through so much that it makes a good introduction to the topic.
The above material gives a teacher everything needed to create a unit on matrices that incorporates spreadsheets. I remember learning matrix when I was in college. I spent so much time with my fingers, one on one, the other finger on another one and just working my way through it. I wish I'd had access to spreadsheets to check my answers or spend time using it to do calculations so I could focus on some real world applications.