Sure, if you're solving a 2x2 in ONE place in a piece of software, it makes sense to just perform the computation directly without using a library.

Realistically speaking, though, if you're doing one 2x2 computation, you're probably going to end up doing a bunch of other linear algebra as well. If you don't do linear algebra in your everyday work, the threshold from rolling-your-own solution to grabbing a library is going to come up very quickly.

The Armstrong example is perhaps a bit mis-titled. He's talking about "implementing from scratch" only insofar as he can use the facilities of his platform to perform exactly the task he needs to do rather than bringing in a huge dependency, in this case, an FTP server that does a lot more than the one task at hand.