So the new core was added by the SymPy crew and it seems much faster than before - at least according to my test cases. Mateusz tells me my module worked out-of-the-box, which is always nice to hear.
I managed to put together a nice (in my opinion) tutorial for my linear algebra pack. Though I will say the inability to have a table of contents of html anchors make it very hard to read and navigate the page. This is usually something quite easily done in a wiki.
The tutorial brought to light a couple of stupid mistakes and inconsistencies I had made so it was helpful in the debug process too.
I'm thinking block LU decomp next week, kind of an advanced thing as we come to the end of the project....