Variation of Coefficients of Simultaneous Linear Equations

Simultaneous equations are of great importance in modern structural engineering, and the purpose of going through a solution is, obviously, to obtain numerical results for a specific set of conditions. It is often of equal importance, however, to know the effect of a change in the geometric and elastic properties of the structure. Without such knowledge it is impossible to study the design with a view toward obtaining the most in economy and certain other desirable qualities. Such studies, except for the simplest structures, can be made only at the expense of re-solving the equations each time a change is made in the coefficients, and the labor involved is so great that studies cannot ordinarily be made except very roughly and sketchily. With the theory presented in this paper, the effect on the solution produced by a change in any number of the coefficients in any one equation, or in any number of coefficients of any one unknown, can be computed quickly and simply in one step.