ABSTRACT
The first part of this chapter deals with systems of linear equations. To solve them in MATLAB they must be written in the matrix form AX = B. Then, the preferred MATLAB solution uses the backslash operator, ‘\’, called as X = A\B. The backslash operator always yields a solution; it can be a unique solution, a particular solution, a solution in the least-squares sense, or no solution at all. To explain these cases we distinguish between fully determined, underdetermined, overdetermined and homogeneous systems. The KroneckerCapelli theorem gives a criterion for knowing whether a given system of linear equations has a solution or not. The criterion is based on the notion of rank, a number that can be calculated in MATLAB.
