初等列变换与线性方程组的换元法求解

Elementary Column Transformation and Solving Linear Equations by Substitution

对线性方程组的增广矩阵作某些初等列变换,相当于对线性方程组用换元法求解.在对增广矩阵作两次互逆的初等列变换之间进行若干次初等行变换,并不改变增广矩阵所代表的线性方程组的同解性质.利用这一特点,可以灵活地运用初等列变换来求解线性方程组.

When some elementary column operations are applied to the augmented matrix of a group of linear equations ,it carry the connotation of solving the group of linear equations by substitution .Between a pair of mutually inverse column operations ,some row column operations can be applied without change of the solution of the equations .Use this feature ,elementary column transformations can be applied for solving linear equations .