含参数线性方程组解的判别方法注记  

A Note on the Discriminant Method of Solutions of Linear Equations with Parameters

作　　者：邢永丽 王迪 XING Yong-li;WANG Di(The School of Science, China University of Geosciences (Beijing), Beijing 100083,China;Technology Department, SAIC Motor Co. Ltd. Shanghai 201804, China)

机构地区：[1]中国地质大学(北京)数理学院,北京100083 [2]上海汽车集团公司技术研究部,上海201804

出　　处：《大学数学》2021年第1期108-111,共4页College Mathematics

基　　金：中国地质大学(北京)2020年度本科教育质量提升计划建设项目(JCJXZZ202007)。

摘　　要：当线性方程组中含有未知参数时,线性方程组解的情况往往需要进行讨论.本文给出了在非齐次线性方程组系数矩阵中含有未知参数且系数行列式等于零的情况下,判定对应参数值下方程组的解是无解还是有无穷多解的两个判定定理.和以前的方法比较,本文提出的讨论方法更直接.When the system of linear equations contains unknown parameters,the solution of the system of linear equations often needs to be discussed.In this paper,two theorems are given to determine whether the solution of a system of nonhomogeneous linear equations has no solution or infinite solutions when the coefficient matrix of the system contains unknown parameters and the determinant of the coefficient equals zero.Compared with the previous methods,the discussion method proposed in this paper is more direct.

关 键 词：线性方程组 系数行列式 矩阵的秩 Λ-矩阵 几何重数 

分 类 号：O172.1[理学—基础数学]