The course is "Linear Algebra with Applications" - and the OP explicitly wanted a course to learn linear algebra for non-math majors. It's not about "doing math

The course is "Linear Algebra with Applications" - and the OP explicitly wanted a course to learn linear algebra for non-math majors. It's not about "doing mathematics" in the sense of doing novel math, it's about learning basic linear algebra and being able to apply it to a non-math field. IMHO for everyone who wants or needs to "learn actual mathematics" there are at least ten people who need "applied mathematics" in the sense of being able to apply well-known theorems from a well developed field (like linear algebra) and with zero need to ever prove anything novel, even trivial things; they need to understand the concepts and know how and where to look up the appropriate formulas to do the linear algebra calculations they need for their non-math domain. This OP wanted a course for the latter need and this course failed at this goal. For a random example I heard recently; there's applications of differential equations in pharmacokinetics, so people studying pharmacokinetics need a sufficient math background for that. However, the appropriate math background for these students involves the general concept of differential equations and being able to understand a couple specific equations which characterize their physical domain, and do calculations involving them. For that use case there is no need for a skill in "doing math" - all the mathematical properties of those particular equations are known and they can and should look them up instead of learning how to derive them from first principles, much less making any new assertions.