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对增广矩阵增行增列以解线性方程组的技术

发表时间:2011-01-15  浏览量:1654  下载量:531
全部作者: 陈必红
作者单位: 深圳大学数学与计算科学学院
摘 要: 提出对增广矩阵加行加列的操作技术,加行的目的是增加增广矩阵的秩,同时加列将使未知矩阵的列数增加以保存完整的方程组信息。通过不断地加行加列并进行高斯消元及去除零行,最后能够在矩阵中产生方程组的通解。操作的通用性有益于教学,也容易通过编程求出方程组的通解,并已经在网站中的解线性方程组的在线计算中得到使用。
关 键 词: 线性代数;矩阵;线性空间
Title: Technology of adding rows and columns to augmented matrix for solving systems of linear equations
Author: CHEN Bihong
Organization: College of Mathematics and Computational Science, Shenzhen University
Abstract: In this paper a technology is proposed that adds rows and columns to the augmented matrix. Adding rows is to increase the rank of the augmented matrix, and adding columns is to increase the column number of augmented matrix to keep entire information of the linear system. By constantly adding rows and columns and deleting zero rows, and finally generating the general solution in the matrix, such method has universal property and is easy to understand and get general solution by programming. It has been used in online calculation of systems of linear equations on the internet.
Key words: linear algebra; matrix; linear space
发表期数: 2011年1月第1期
引用格式: 陈必红. 对增广矩阵增行增列以解线性方程组的技术[J]. 中国科技论文在线精品论文,2011,4(1):77-81.
 
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