Inspired by the recent success of my "soft question" here, I also have to ask, what are some of the oldest linear algebra books out there with exercises? I'm fine with or without solutions, either way.

Again, maybe there are some hidden gems from before the 20th century out there.

Why am I hunting for the oldest sources possible? Well, two very well-known mathematicians who have recently passed (Abhyankar, Voevodsky) and a well-known living physicist (Wolfram) told me to read Grassmann in order to learn linear algebra properly and not be corrupted by the "postmodern turn" in mathematics where the original means and ends of linear algebra have been separated.

I've attempted reading Grassmann's work before, but I would really like a textbook written as close to his lifetime as possible on linear algebra that has exercises.

calledlinear algebra. For example there are old books on "matrix theory" but they don't cover exactly the same set of topics that we currently think of as "linear algebra," nor do they think of the subject as being about transformations of vector spaces over a field. So asking for pre-20th century "linear algebra" books may be somewhat anachronistic. – Timothy Chow Oct 28 at 18:24