More commonly the problems of engineering lead to a large system of linear equations. The numerical solution of these equations involves the matrix inversion; the right hand sides of these equations being either fixed or variable. In case of right hand sides being fixed column vectors, the Guassian elimination and back substitution is the simplest and quickest way to solve the linear equations. However, in cases when the right sides are variables in many engineering applications in general and structural analysis in particular, a search has to be made for an efficient method, both, in terms of computational execution time as well as computer storage. Several problems were solved using different alternatives in order to arrive at the most economical solution.