I'm dealing with systems of 3 differential equations that are all coupled to each other. Fortunately, all the ODEs are first order. Can somebody give me a primer of how to use matrices to solve these problems? here's an example: Say we have a system of 3 ODEs all coupled to each other: Mx, My, Mz dMx/dt = A*Mx + B*My + C*Mz dMy/dt = D*Mx + E*My + F*Mz dMz/dt = G*Mx + H*My + J*Mz So the matrix would be: dM/dt = [A B C D E F G H J] M + [K L M] So what do I do now? Diagonalize the matrix and then find eigenvectors? Whats the step by step?