The need to solve large linear systems of algebraic equations arises in almost any mathematical model, as illustrated in the instances below. In particular, we go into some detail regarding electrical networks. The most common method used to solve such linear systems is based on factorization of the matrix in triangular factors, which is discussed and shown to be equivalent to the Gaussian elimination method (learned in almost any elementary course in algebra).

We present this method in a form that can be the basis for a computer algorithm. When one wants to solve very large systems of equations, it is important to know how computational complexity grows with the size of the problem. This topic is also addressed, including the case where the matrix has a special structure in the form of a bandmatrix. The solution of tridiagonal systems is considered in particular detail. In addition, some basic dimension theory for matrices, such as the relation between rank and the dimension of the nullspace, is discussed and derived using the factored form of the matrix.