用矩阵列初等变换法求解非齐次线性方程组

摘 要:利用矩阵的初等列变换解非齐次线性方程组,这种方法在许多情况下应用起来比较方便.本文给出了一个命题，对于任意的矩阵C，对其做初等列变换，变成一个两部分的分块矩阵，左边是列满秩的子块，右边是零矩阵，对于一个单位矩阵做同样的初等列变换，右边将是其次线性方程组CX=0的基础解系.在此命题的基础上，可以用初等列变换来求解线性代数的许多计算题，也可以证明一些线性代数的定理.本文还将揭示，在求解非齐次线性方程组的时候，矩阵的列变换方法更加容易学习，更容易理解. 关键词: 矩阵; 初等列变换; 线性方程组

To solve linear equation using matrix elementary columu vary

Abstract : To solve linear equation using mat rix elementary column vary, this method is very convenient under different circumstances. This paper gives and proofs a theorem,for any matrix C, do elementary column operations, chang it to a matrix which is partitioned to two submatrices which left one is column full rank and right one is zero matrix. Then do same elementary column operations to a unit matrix with same column number as C, and do some partition to the result, then right submatrix of it, is just basic solution set of homogeneous linear equation CX=0. On the basic of the theorem, lots of problems of linear algebra can be resolved and lots of theorems can be proofed by elementary column operations. The paper will reveal that them will not easy to learn and to program and to proof something as techniques giving by the paper.

Key words : mat rix ; elementary column vary ;linear equation.