I'm all for teaching programming... but I'm not sure you can do a respectable job of python in the time you'd have in a course like this. If you did, I'd teach a small subset, like python's turtle library.

Slow down there. Solving an NxN system of linear equations is a O(n^3) operation in the dense case. (Yes, you can speed it up with LU decomposition(if you want to solve the same matrix with lots of b matrices) for an O(n^3) once and O(n^2) after that, or might be able to get a better iterative scheme(though you can't really plan on it).) Your point still remains about not being NP-complete or NP-hard. But it's one more thing we could do with quantum computing, and I'd still be pretty satisfied with myself if I could take an O(n^3) to O(log n).