Good luck with the LA book. It is a beautiful subject with so many applications, so a great opportunity to do an original take on it.
In case this is might be helpful, here is a preview of the LA book I wrote[1] and the condensed four-page-in-small-font tutorial version[2]. You might also consider using a computer algebra system for teaching, see [3] for my take on LA using SymPy. Last but not least, I highly recommend the CMapTools software for creating concept maps, which can really summarize the field in a very compact form[4].