ABSTRACT

This and the next two chapters contain the basic methods for solving matrix equations of the form Dx = d where D is a matrix and x and d are column vectors. A much more complete description of solution methods and linear algebra can be found in [5]. The possibilities of a unique solution, no solution, multiple solutions and least square solutions are discussed. In this chapter most of the algebraic systems are assumed to be square so that the number rows (equations) and columns (variables) are equal. Row operations and elementary matrices are used to do by-hand computations of the Gauss elimination, LU factorization and inverse matrix methods. These methods are also implemented in MATLAB. Applications to steady state circuits, mixing tanks, heat conduction and support trusses are given.