一种解线性方程组的新方法

A New Algorithm for Solving Linear Equations

利用初等行变换给出了线性方程组的一种新解法,此方法可以直接得到齐次线性方程组的一个基础解系;对于非齐次线性方程组,此方法不仅可以判断方程组是否有解,而且在有解时还可以同时得到方程组的一个特解和对应的齐次线性方程组的基础解系.

By using elementary row transformation a new algorithm is proposed to solve linear equations in this paper. The new algorithm not only can obtain a system of basic solutions of the homogeneous linear equations but also can judge whether the non-homogeneous linear equations have its solution or not. Moreover, a particular solution of the compatible linear equations and the basic set of solutions of the corresponding homogeneous linear equations can be got simultaneously.