To make a three phase generator you have to place a certain number of magnets on your stator and armature, all with proper spacing. Electromagnetism is as complex as dealing with waves and water, so you need to know how to control the field through your design.
1 Know if an ordered pair is a solution to a system of linear equations in two variables or not. 2  Solve a system of linear equations in two variables by graphing. 3  Solve a system of linear equations in two variables by the substitution method.  Solve a system of linear equations in two variables by the elimination method.
No idea how to solve differential equations analytically with matrices, however, numerically solving a differential equation definitely involves matrices. If we talk about partial differential equations and system of ordinary differential equations then there matrix method are used to solve homogeneous linear equations with constant coefficient.