基于线性方程组整体消元过程的行列式知识构建  

Determinant Knowledge Architecture Based on Procedure of Eliminating Variables in Linear Equation System

作　　者：王永革 马健[1] WANG Yongge;MA Jian(School of Mathematical Science,Beihang University,Beijing 102206,China)

机构地区：[1]北京航空航天大学数学科学学院,北京102206

出　　处：《河南教育学院学报（自然科学版）》2023年第4期53-59,共7页Journal of Henan Institute of Education(Natural Science Edition)

基　　金：教育部首批新文科研究与改革项目(2021100006);教育部基础学科拔尖人才培养计划2.0研究课题重点项目(20211009);北京航空航天大学线性代数教改项目。

摘　　要：给出线性方程组整体消元求解的一种方法。基于整体消元过程,自然引入行列式定义、展开定理及克莱姆法则等行列式核心概念。通过线性方程组消元求解这一共同背景,分析行列式主要知识点的含义及其内在联系。A method to solve linear equation system by leaving only one variable and eliminating all other variables is provided.In the procedure of eliminating variables,some important concepts about determinant including the definition of determinant,the number of inversions,algebra cofactor,Laplace′s Expansion Theorem and Cramer′s Rule are introduced.And these concepts′meaning and their relationship are shown based on the method.

关 键 词：线性方程组 消元过程 行列式定义 逆序数 拉普拉斯展开 知识构建 

分 类 号：O151.2[理学—数学]