线性方程组的求解方法与应用

湖北民族学院理学院2016届

本科毕业论文(设计)

线性方程组的求解方法及应用

学生姓名： 付世辉 学 号： 021240712 专 业： 数学与应用数学 指导老师： 刘先平 答辩时间：2016年5月22日 装订时间：2016年5月28日

A Graduation Thesis (Project)

Submitted to School of Science, Hubei University for Nationalities

In Partial Fulfillment of the Requiring for BS Degree

In the Year of 2016

The calculation method and application of the system of linear

equations

Student Name: Fu Shihui Student No.: 021240712 Specialty: Mathematics And Applied Mathematics Supervisor: Liu Xianping

Date of Thesis Defense: 2016.05.22 Date of Bookbinding: 2016.05.28

摘 要

线性方程组在数学领域中的应用非常广泛，是线性代数的主要内容之一. 矩阵及其基本理论是学习线性代数的一种基本工具，矩阵的初等变换则是线性方程组求解的工具. 线性方程组常用的求解方法有一般消元法、克拉默法则、LU分解法等一系列方法，根据问题的不同，我们在求解的过程中选择的方法也就多种多样. 这些方法可以很好地解决线性方程组的求解问题，在求解过程中，向量和矩阵起着一个不可或缺的作用. 在线性方程组的应用方面，除了跟数学理论知识有着密不可分的联系，还和我们的实际生活联系的极其紧密.

关键词：线性方程组，矩阵，初等变换，克拉默法则，LU分解法

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Abstract

Linear equations are widely used in the field of mathematics and they are the main contents of linear algebra. The Matrix and its basic theory are basic tool for learning linear algebra, the elementary transformation of the matrix is the tool of the solution of the linear equations, the commonly used methods of solving linear equations have the general elimination method, Gramer, the LU decomposition method and so on, is according to the problem, we choose one from a variety of method in the process of solving. These methods can solve the problem solving linear equations, vectors and matrices play integral roles in the process of solving. In the application of linear equations, it has not only a close link to the knowledge of mathematical theory, but also very close to our real life.

Keywords: linear equations, matrix, elementary transformation, Gramer, the LU decomposition method

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