I’m tutoring a kid in Algebra II. He’s having trouble with matrices. He is unable to report what exactly it is he needs to know about them for the test he’ll be (re)taking. So all I have to go on is his textbook.
The textbook has a chapter section or two on solving systems using matrices which seem to presuppose that the student knows a way to find inverses of 3x3 matrices. But going back to the chapter section on 3x3 inverses, I find only a method for verifying that two matrices are inverses, and no method given for actually finding the inverse. No surprise, since finding the inverse of a 3x3 matrix can be very difficult.
Yet as I said, future chapter sections seem to presuppose that the student should be able to find the inverse.
So one fairly easy method for finding inverses for certain tailor-made examples is the method using [url=http://www.purplemath.com/modules/mtrxinvr.htm]row operations*. When I briefly described this method to the student he said it “sounded familiar” which I take to be a clue that this is the method his teacher uses in class and will be using to generate inverse problems on the exam. So I’m thinking I’ll review the method with the student next time, but for that, I need some of those tailor-made examples I mentioned. Which brings me to the question–is there a good source online for such examples? I can’t find one.
I’m kind of reminding myself about matrices as we go on this one, so if something I’ve said above makes you think there’s some important info I’ve forgotten since high school that would be good. The textbook the student is using seems to be written with the expectation that a lot of explanation will come from the instructor from the course. As such, the book seems very incomplete in many ways. In any case, I was unable to glean much info from it–it seemed opaque, not because of density but because of missing presupposed knowledge.