[verylongaccount]

I am a big fan of Hoffman and Kunze. I also think many would benefit from reading a book on ordinary differential equations after they read a linear algebra textbook. Much of the elementary theory of linear ODEs consists of combining relatively simple observations with linear algebra. Coddington and Levinson is the one I used for a course in college, but it is quite detailed. I am sure there are less ponderous options available, but I don't know any off the top of my head.