关于克莱姆法则推论的证明补充

克莱姆法则是解线性方程组的根本法则。不管使用什么工具(比如矩阵),最后解决问题仍然是克莱姆法则。同济版《线性代数》在给出推论的必要条件后虽然也指出了条件是充分的,但基于章节的安排,在没有建立线性方程组解的理论的前提下,还不能给出充分条件的证明。为了方便应用,本文给出两种克莱姆法则推论的证明补充。

Cramer＇s Rule is a fundamental rule for solving linear equations. No matter what tools are used, such as matt, the final solution to the problem is still by Cramer’s Rule.《The Linear Algebra》 , which published by Tongji University, gives a necessary condition about deduction of the Rule. Due to the arrangement of the chapters, it is just pointed out that the sufficient conditions which hasn＇t been proved are established. Because the theory of linear equations haven＇t been provided. In this naner. Two kinds of methods are given.