Polling recent mathematics graduates might lead oneto conclude that Markov processes, curve fitting, andsystems of ODEs are the main applications for linearalgebra. But thanks to the simplicity of linear models,one does not have to look hard to find solutions to manyother applied problems that employ linear algebra in asignificant way. In this talk I will outline three morescience problems, the physics of spinning objects,"dimensional analysis", and the spectroscopic examinationof chemical solutions, for which fundamental ideas fromlinear algebra provide amazing clarity.