The Linear System Analyzer (LSA) is a component-based problem-solving environment (PSE) for the manipulation and solution of large sparse linear systems of equations. Both the underlying component infrastructure and its application to the problem area of linear systems are introduced. Initial results indicate the utility of clearly separating the PSE infrastructure from the particular problem domain(s) which use it, leading to a resuable PSE builder. The component approach provides coarse-grain parallelism between components, allowing larger problems to be solved by simultaneously using the computational resources of multiple machines. Furthermore, the LSA system allows side-by-side comparisons of methods and rapid experimentation to develop practical solution strategies.