齐次线性方程组解空间的性质及应用  

Properties and Applications of Solution Space for Homogeneous Linear Equations

作　　者：贾宏宇 张淑娜 陈衍峰 JIA Hong-yu;ZHANG Shu-na;CHEN Yan-feng(School of Mathematics,Tonghua Normal University,Tonghua 134002,China)

机构地区：[1]通化师范学院数学学院,林通化134000

出　　处：《通化师范学院学报》2020年第10期40-44,共5页Journal of Tonghua Normal University

摘　　要：文章对齐次线性方程组的基本理论进行简要阐述,并研究了齐次线性方程组在初等数学中证明等式、证明三角恒等式、求值及数量关系中的应用,以及在高等数学中的判断向量组线性相关性、证明行列式等于零、证明矩阵秩中的应用.通过研究齐次线性方程组在初等数学及高等数学中的应用,充分体现了线性方程组理论的实用价值.In this paper,the basic theory of linear equations is briefly explained,and the theory of homo⁃geneous linear equations is applied to solve some problems in elementary mathematics and higher mathe⁃matics,which makes the connection between theory and practice more closely,and fully embodies the practical value of the theory of linear equations.

关 键 词：齐次线性方程组 矩阵的秩 非零解 

分 类 号：O151[理学—数学]