On this page you can find a set of videos, created by Dr James Tanton, for topic AHL 1.15, raising matrices to large powers using eigenvalues and vectors to diagonalise the matrix (a powerful application of which is Transition matrices and Markov Chains - AHL 4.19). Eigenvalues and vectors, have many other applications (explored here: coupled differential equations and Phase portraits)See the structured, student notes...