The introduction of matrix formulations is heralded both as a notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and Gauss’s row reductions. Inverses are studied first in this operator context before addressing them computationally. The determinant is cast in its proper light as an important concept in theory, but a cumbersome practical tool. Projects include matrix aspects of finite difference modeling, Kirchhoff’s circuit laws, GPS systems, and fixed-point methods.