Cool Matrix Multiplication!

August 6, 2012

I had marked this post in my Reader feed to bookmark later, but Sam’s recent post inspired me to post about it sooner, rather than later.

For some unknown and mysterious reason, I have always loved matrices. Maybe it’s because my high school let me take it as an independent study class when I was a junior, or maybe because as a slightly-OCD-type person, I like seeing the numbers all nicely lined-up. Love of matrices also worked well in the 23+ years I spent as a database programmer (FOR-NEXT loops and 2-dimensional arrays are your friends).

Since I began teaching math eight years ago, and hooking back up with matrices and matrix operations, I was somewhat distressed to learn that I have forgotten a lot of what I used to know; moreover, I have a horrible time remembering the quirks for multiplication. This is why I think CalcDave’s post is so brilliant. Lookee:
Why didn't I ever think of this?

This makes so much sense! It also makes it easy to spot when the multiplication won’t work. I just wish matrices got more respect. The Texas standards (TEKS) for Algebra II only mention matrices once, and that is in the context of solving systems of equations (which means using a calculator). **sigh**

I teach Algebra III, which is an elective course that is designed to a) address the needs of students who are on an honors track, but aren’t ready/willing/able to take Precalculus and b) make sure students are prepared for College Algebra. Because it is an elective and there are no state standards, I have a pretty free rein in what I teach. I usually do a mini-unit on matrices, but not in very much depth. I think this method is inspiring me to maybe stretch it out a little more. From a placate-the-administrator standpoint, there are some nice TEKS (standards) for an elective course called Advanced Quantitative Reasoning that explicitly mention arrays and matrix manipulation that I might want to look into.

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