Lec 28 MIT 18.03 Differential Equations, Spring 2006
The real topic is how to solve inhomogeneous systems, but the subtext is what I wrote on the board. I think you will see that really thinking in terms of matrices makes certain things a lot easier than they would be otherwise. And I hope to give you a couple of examples of that today in connection with solving systems of inhomogeneous equations. Now, there is a little problem. We have to have a little bit of theory ahead of time before that, which I thought rather than interrupt the presentation as I try to talk about the inhomogeneous systems it would be better to put a little theory in the beginning. I think you will find it harmless. And about half of it you know already. The theory I am talking about is, in general, the theory of the systems x prime equal a x. I will just state it when n is equal to two. A two-by-two system likely you have had up until now. It is also true for end-by-end. It is just a little more tedious to write out and to give the definitions. Here ...