You don't really need those calc courses to learn linear algebra. It's more about "mathematical maturity": familiarity with vectors, functions, inverse functions, a general intuition about multidimensional coordinates, and so on. A programming background would probably go a long way (although I don't speak from experience; I learned a lot of math before I started programming).

It's hard to overstate the importance of linear algebra in software. It's really worth learning.

Calculus gets a bad rap for being difficult, but if you're learning on your own, you can just focus on the ideas and not on the arduous computation (which something like maxima can do for you). The core ideas of calculus can probably be learned in a week. Review all the trig on Khan Academy, then try watching some calculus lectures, focusing on the big ideas, not memorizing rules for computing derivatives or integrals.

BTW, you probably don't need much calculus to learn most of the linear algebra you need; those requirements are mostly there for mathematical maturity, plus then being able to assign more interesting exercises.

Don't look at the prerequisites and dig right in. I don't think you'll have any problems. Linear Algebra is something that kinda stand on its own.

> this is what my whole Dependency chain looks like

You should not think like that when learning. If you want to be efficient just take shortcuts.

Learn machine learning (btw there are great courses on coursera or Stanford about that), and if you're stuck on something just check on wikipedia or another resource.