克拉默法则的一个简单证明及其推广

天津农学院学报 ›› 2013, Vol. 20 ›› Issue (3): 42-44.

克拉默法则的一个简单证明及其推广

陈成钢

天津城建大学理学院,天津 300384

收稿日期:2013-03-29 发布日期:2019-10-21
作者简介:陈成钢（1976-）,男,山东菏泽人,副教授,硕士,主要从事高等数学教学及概率统计应用方面的研究工作。E-mail：chenggangchen@yeah.net。
基金资助:
天津市教委2012年重点教改课题"‘卓越计划’下数理基础课程教学改革的研究与实践"（C04-0832）

A Simple Proof of Cramer Rule and Its Promotion

CHEN Cheng-gang

Department of Sciences, Tianjin Chengjian University, Tianjin 300384, China

Received:2013-03-29 Published:2019-10-21

摘要/Abstract

摘要： 给出了线性代数教科书中克拉默法则的一个简单证明。对于系数矩阵A是方阵的线性方程组Ax = b,当其有唯一解的时候,能利用克拉默法则求解。但当A不是方阵,克拉默法则则无法求解,其实利用矩阵秩的理论可以将克拉默法则进行推广,使其能求解任意有唯一解的线性方程组。

关键词: 线性方程组, 唯一解, 克拉默法则, 秩

Abstract: It is given a simple proof of Cramer Rule in Linear Algebra textbooks. As we all know, system of linear equations can be solved by means of Cramer Rule when its coefficient matrix is a square matrix and it has a single solution. But it is powerless for Cramer Rule to solve when its coefficient matrix isn’t a square matrix. So, it is promoted Cramer Rule to solve the arbitrary system of linear equations as long as it has a single solution.

Key words: system of linear equations, single solution, cramer rule, rank

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