线性方程组的标准形
首发时间:2012-02-09
摘要:一个矩阵称为标准形矩阵,是指的它是由单位矩阵再可选地添上一些零行在下边或零列在右边构成的矩阵。任给一线性方程组Ax=b,对系数矩阵A作初等变换变成标准形矩阵D=PAQ, 其中P与Q都可逆,得到的另一个线性方程组Dx=d,称这样的线性方程组是标准形方程组。本文研究了标准形方程组有解的充分必要条件,给出了通解的结构,与原方程组的通解的线性关系,从而给出了另一种解线性方程组的技术,并能够容易地证明一些已知的结论,这样有利于使线性代数课程的教学方案更为简洁,还能够在线性方程组的基础理论方面取得进展。
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The Standard Form of Linear Equation System
Abstract:A standard form matrix is a identity matrix or optionally adding some zero rows at bottom or zero columns at right. Any linear equation system Ax=b can lead to another linear equation system Dx=d in which D is a standard form matrix and D is got by doing elementary operations to A so D=PAQ and P and Q are inversable matrix. Such linear equation system Dx=d is called as standard linear equation system. The resolutionable condition, solution set and linear relationship to solution set of original system of the standard form of linear equation system is researched in this paper, so that another technolege to resolve linear equation sysytem is given, and some facts can be proofed more easily, so it is helpful to let teach plan of linear algebra course to be more simble, and could get progress in base theory of linear equation system.
Keywords: linear algebra linear equation system standard form
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