It is noted that, for both explicit and implicit linear systems, several observer design problems, including system inversion, for systems with or without unknown inputs can all be formulated as a single problem involving descriptor systems. The method used for solving this problem is based on recursively applying the reduction operation which consists of identifying and discarding equations that do not provide useful information for the estimation problem. The reduction algorithm produces a reduced dimension system for which standard observers can be constructed. The method presented can be implemented using numerically robust algorithms. One such algorithm is presented.