In games you're probably applying many small inverse matrices to many small vectors. In partial differential equations, you solve a single large linear system where the unknown vector represents a field defined at every point on a spatial mesh.

In my research, specifically, that spatial mesh can have as many as 10^7 grid points. For linear systems of this size, any exact solution at all is impractical - we exclusively employ iterative approximations built from terms of the form (A^n) b since matrix-vector products are about the only things we can compute in a reasonable amount of time.