关于体上非齐次左线性方程组解的研究

给出了任意体F上非齐次左线性方程组相容的一个充要条件和求解的简便方法,利用此法还能同时求出其导出组的基础解系,而且顺便讨论了F上一般左线性方程组的解,给出了其有解判定定理及解的结构定理。

Some Studies on Solution of a Nonhomogeneous System of Linear Left Equations Over a SkewField

In this pqper we give a sufficient and necessary consistency condition of a nonhomogeneous system of linear left equations over an arbitrary skew field F, and a convenient, simple method of solving the system. By the method, we can also find a fundamental system of solutions of the associated homogeneous system. By the way, we discuss solutions of a general system of linear left equaions over F, give a theorem on the consistency criterion of the system, and a theorem on its solution construction.