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It is a very practical field of math, especially for computer scientists (Graphics, some variants of machine learning, pretty much any large scale computation with chunks that can be processed in parallel), which is probably where people derive importance from. Another huge benefit is that linear algebra (For matrices with certain properties, not generally) often allow for iterative and approximate solutions, which can make linear algebra a more tractable computational route. Some of your engineering classes may have used numerical solvers that rely on linear algebra to iteratively obtain relatively precise solutions to difficult equations.

You are correct that the fundamentals (Vectorized computation, aka matrices) are often introduced early on. The level at which you interface with linear algebra often scales with the level of math you are at. You can add them [1], integrate them [2], and use them to solve some PDEs [3]. You can see how all these "levels" of linear algebra would be accompanied by another math class pushing you to utilize linear algebra at a higher level than before. It appears that you're at the first level. I've actually never done [2] in the classroom, but [3] was introduced to me in a class on differential equations that utilized matrices as a possible solution route.

If you are interested in learning more, Khan academy has good linear algebra videos.

[1] http://www.purplemath.com/modules/mtrxadd.htm [2] https://www.youtube.com/watch?v=z73ed-bd9ek [3] http://www.maths.manchester.ac.uk/our-research/research-grou...

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