用递归定义推导行列式的展开法则及有关性质

DEDUCTION OF THE EXPANSION AND THE RELATED PROPERTIES OF DETERMINANTS WITH RECURSIVE DEFINITION

用递归定义证明了“行列式相邻两行对调，其值变号”的性质，并根据这一性质推导出了行列式的按行展开法则及有关性质，从而简化了传统的推导方法．

In this paper, the property is proved that if two adjacent rows of the determinant are interchanged, the sign of the determinant is reversed. According to this property, we introduce a rule regarding to expand determinants by the row and some related properties. Thus the traditional method is simplified.