Matrices are absolutely *critical* to 3d graphics, and any non-trivial 2d graphics. Those photoshop plugins are *heavily* based on linear algebra.
The code might not be written in mathematical matrix form, or be hidden behind libraries, but if you have 3-vectors (i.e. points relative to the origin in 3-space), any global linear transformation is represented by a matrix multiplying each vectors. Rotation, skew, scale, projection (shadows and reflections) and scaling are all linear transformations.
It's like saying matching text doesn't require state machines. It does, you've just never used them in their raw form. Meanwhile, learning the actual theory of how regular expressions and compilers actually work requires that you understand state machines (because that's what lex and yacc actually spit out, or what your higher level language actually dynamically constructs based on the regex). Likewise, understanding the core theory behind computer graphics necessitates learning linear algebra.
On the other, I can now rephrase my question thusly: "in terms of what other system could we try to explain the observed phenomena that we call entanglement?"
Math. Specifically, complex linear algebra.
Machines certainly can solve problems, store information, correlate, and play games -- but not with pleasure. -- Leo Rosten