Linear algebra is basically the foundation of most serious computation effort. We rank supercomputers essentially by their sustained floating-point computation rate solving large linear equations--a substantial fraction of HPC workloads boil down to "math on large matrices." In the large scale, basically any simulation (whether it be weather modeling or analysis of the stress on a physical object) is solving linear equations. Graphics tends to boil down to doing lots and lots of small matrix multiplications, as does signal or image processing. Optimization problems also tend to boil down to linear algebra as well (via simplex)--so things like operations research, place & route on FPGAs, or even optimal factory ratios in a game like Factorio turn out to need to use linear algebra.