摘要
根据基变换公式以及过渡矩阵的可逆性,证明了同型矩阵行等价为矩阵的行向量组等价的充分必要条件,另以引理极为简单地证明了同解线性方程组的重要结论,由此给出了线性方程组从自由未知数到非自由未知数的映射唯一性。可以对有关理论的细节作出补充,解决了现有教材中在分析有关内容时尚未完备讨论的问题。
This paper primarily demonstrates,based on the fundamental transformation formulas and the inver-tibility of transition matrices,that the row equivalence of similar matrices is both a necessary and sufficient condition for the equivalence of their row vector sets.Moreover,a lemma is used to simply prove an important conclusion regarding the solutions of linear equations.Consequently,it establishes the uniqueness of the mapping from free variables to non-free variables in linear equation systems,and provides supplementary details on the relevant theories,thus addressing the inadequacies in the discussions presented in current textbooks on the subject.
作者
谭俊宇
王培颖
TAN Junyu;WANG Peiying(College of Business Administration,Guangzhou Institute of Science and Technology,Guangzhou Guangdong 510540;College of General Studies,Guangzhou Institute of Science and Technology,Guangzhou Guangdong 510540)
出处
《长治学院学报》
2025年第5期64-66,103,共4页
Journal of Changzhi University
基金
广州理工学院校本研究项目“《线性代数》优质课程”(2024XYZK15)。
关键词
同解
线性方程组
行向量组
行等价
simultaneous solution
system of linear equations
row vector sets
row equivalence
