Solving Simultaneous Equations

Abstract

Our view of the universe is shaped by the way we look at it. Traditionally, the physical world has been treated as a system in which one independent variable acts with one dependent variable while the rest of the universe exists in an imaginary state of suspended animation. Reality is not that way of course, but it is unfair to suppose that physical scientists have failed to consider functions of many variables out of ignorance; the mathematical difficulties were simply too large to do it any other way. With the advent of the computer, systems of many variables can be studied and the impact of this technological advance will certainly be large. This chapter considers systems of many variables, in principle, indefinitely many, under the constraint that some dependent variable is a linear function of all the independent variables. As such it is an introduction, for nonlinear multivariate systems should also be studied. We will leave that for another book, however, with the comment that the principles will be the same, only the mathematical complexity will be increased.