摘要
首先讨论了两个齐次线性方程组有非零公共解的充分必要条件并给出了非零公共解的一般形式,然后讨论了两个线性方程组同解的一个充分必要条件和非齐次线性方程组的线性无关解向量的个数以及非齐次线性方程组通解的表达式,最后证明了非齐次线性方程组有解的一个充分必要条件.
This paper has anlyzed the sufficient and necessary conditions of the phenomenon--two homogeneous linear equation groups have a not zero public solution, and provided a general form of the not zero public solution . This paper also discussed one sufficient and necessary condition of the same one solution which two linear equation groups have, the number of linear irrelevant solutions and the expression formula of general solution to heterogeneous linear equations. Consequently, it can be proved that there exists the sufficient and necessary condtions of the phenomenon--heterogeneous linear equation groups have a solution.
出处
《大学数学》
北大核心
2008年第4期157-161,共5页
College Mathematics
基金
安徽省精品课程<经济数学基础>研究成果
关键词
线性方程组
基础解系
特解
通解
非零公共解
linear equation group
a group of basic solutions
special solution
general solution
not zero public solution
