求解线性方程组的方法探讨摘要：线性方程组在数学领域中的应用十分广泛，而且它的求解方法在代数的学习中有着重要的作用，线性方程组的求解方法与行列式、矩阵、线性变换、向量组的线性相关性有着很大的关系，而在《高等代数》中只介绍了高斯消元法以及克莱姆法则，所以解法比较单一，有一定局限性。本论文首先对课题的背景、意义、国内外研究状况进行阐述。而后介绍其概念和他的性质定理。然后对线性方程组的求解方法进行归纳和总结。在例题中说明对每种解法的步骤及其特点，并对各种方法的优缺点、适用性进行分析。线性方程组的解法虽多，但是根据线性方程组的不同结构来选用合适的解题方法，才能提高解题的效率，更快更好的得到结果。关键词：线性方程组；矩阵；初等变换；高斯消元法Discussion on Methods of Solving Linear EquationsAbstarct:Linear equations are widely used in mathematics,and its solution plays an important role in learning algebra.The method of solving linear equations has a great relationship with determinant,matrix,linear transformation and linear correlation of vector groups.However,only gauss elimination and Cramer's Law are introducedin Advanced Algebra,so the solution is relatively simple and has certain limitations.Firstly,this paper expounds the background,significance and research status at home and abroad of the subject.Then the concept and his property theorem are introduced.Then,the methods of solving the linear equations are summarized.In the examples,the steps and characteristics of each method are explained,and the advantages,disadvantages and applicability of each method are analyzed.Although there are many solutions tolinear equations,only by choosing appropriate solutions according to different structures of linear equations can we improve the efficiency of solving problems and get better and faster results.Key words:linearequations;matrix;Elementary transformation;gausselimination目录1.1线性方程组的求解的背景及意义......1.2线性方程组国内外研究现状及评价·122.2线性方程组有无解的判定定理)2.3线性方程组的解的结构....32.3.1齐次方程组的解的结构..32.3.2非齐次方程组的解的结构..3.1高斯消元法......573.3克莱姆(Cramer)法则...·83.4逆矩阵解法103.5分块矩阵解法5-)123.6齐次线性方程组的基础解系求解方法.·133.7非齐次线性方程组化为齐次线性方程组方法网.…1417181.绪论1.1线性方程组的求解的背景及意义线性方程组求解在中国有着悠久历史，对线性方程组的研究，中国比欧洲至少早一千多年，记载于我国古代第一部数学专著《九章算术》的方程章。现行的《高等代数》及线性代数教材中只用高斯消元法和克莱姆法则来求解线性III