Knowledge base plays an important role in intelligent systems. In this paper, we propose a knowledge model of relations and operations, called Rela-Ops model. This model is built based on object-oriented approach, and it has the foundation which are concepts, relations, operators and inference rules. Each concept is a class of objects. It has the structure and behavior to solve problems on its own. Besides that, we also propose the model of problems on Rela-Ops model. Algorithms for solving them are also designed. These algorithms use the combining knowledge of relations and operators in their reasoning processing. Rela-Ops model is applied to build the knowledge base of the intelligent problems solving system in linear algebra. This system satisfies requirements of an intelligent problem solver in STEM education. It can solve exercises about matrices, linear equations systems and vector spaces automatically. Its solutions are step-by-step and human-alike solving methods.