Rediscovering Determinant Expansion on Row or Column Theorem Through Plausible Reasoning

Plausible reasoning is an important approach to reasoning conclusions. In order to cultivate students’ habits and abilities to use plausible reasoning, we should give the students a chance to imitate and practice plausible reasoning in our teaching. For our linear algebra course, most of the definitions and theorems in popular linear algebra textbooks are given directly. Thus, we give a concrete process that rediscovers determinant expansion on row or column theorem through plausible reasoning during our teaching to give the students the chance to learn the reasoning.