Gross's review of linear algebra from his MIT algebra course bridges the gap: http://wayback.archive-it.org/3671/20150528171650/https://ww.... A combination of that and then chapter 11 in D&F should cover whatever readers didn't get from Strang.

That being said, Axler is an excellent book. I don't know if I would replace Strang with it, but I should add it as a supplement to the next edition of this guide!