Take a look at https://demo.webwork.rochester.edu/public/courses/linear_algebra/ (the moodle version has more context for the course).
This is a course in matrix linear algebra and ODE that is usually taught
using Lay or Goode as a textbook. I originally designed it for Strang's linear algebra text (with additional notes on 2nd order constant coefficient ODE) but then retreated to using Lay since Strang was a little too eccentric for my colleagues.
Take a look at the problems -- I think you could still use them in conjunction with the Strang textbook -- I'd be happy to help write additional problems to fill in any gaps.
This file will get you started. The set definition files mostly point to library problems. They may also point to some local problems that are missing. Let me know about those and I'll go track them down. In order to get this out quickly I did not do any checking.