Crazy Math

I have been struggling through an online linear algebra course for five weeks with some of my colleagues at work. My brain is not as sharp as it once was, and of course my memory never was. Still, I like learning and solving problems. I finally got the payoff when I was able to use:

to change this:

to this:

I couldn't explain how this works to save my life, but it is amazing to me that someone figured it out. Math can be cool.