非齐次线性方程组的同解类

The Sorts of Same Solution for Solvable Nonhomogeneous Linear Equations

两个n元有解的非齐次线性方程组同解的根本原因是什么?为了回答这个问题,首先引入线性空间的子空间的陪集概念,然后证明了F^n的陪集的一个重要性质,最后给出了两个n元有解非齐次线性方程组同解的充分必要条件,从而完善了线性方程组的同解性理论。

By introducing frrst the concept of coset in the sub - space of linear space, we have testified an impertant property of the coset and finally give the necessary and sufficient condition for the same solution of the solvable nonhomogeneous linear equations.