[cabinpark]

Linear algebra is insanely important. I would consider the most important area of numerical mathematics to know. Any sort of mathematical modeling you do is going to involve linear algebra at some point.

I have argued that almost all numerical mathematics, in some form, can be modeled as a linear algebra problem. Google's original page rank algorithm is linear algebra. Remember that Netflix challenge? All linear algebra. Optimisation? Linear algebra. Want to do any engineering of a system? Behind the scenes it is all linear algebra as every single numerical technique for solving PDEs, that I am aware of, can be thought of in a linear algebra sense. Fluid modeling is all linear algebra. A lot of the machine learning I've seen is just linear algebra. I would also that almost every simulation running on the world's supercomputers involves linear algebra.

Do you absolutely need linear algebra to do this things? No. Just like I don't need to understand how my car works to drive it. But having an understanding how these systems operate can really help you use them in a more logical way.