一个关于克拉默法则及其逆命题的注记.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(2), 127-132 Published Online March 2017 in Hans. /journal/aam /10.12677/aam.2017.62014 A Remark on the Cramer Rule and Its Inverse Proposition Zhibin Du School of Mathematics and Statistics, Zhaoqing University, Zhaoqing Guangdong th th st Received: Feb. 26 , 2017; accepted: Mar. 18 , 2017; published: Mar. 21 , 2017 Abstract Solving the systems of linear equations plays an important role in higher algebra and linear alge- bra. Cramer rule uses determinant to characterize the existence and uniqueness of solutions of systems of linear equations, which can be applied to the systems of linear equations containing the same number of linear equations and unknown variables, and it is of remarkable theoretic value. In this paper, we will present an alternative proof for Cramer rule by using the properties of de- terminant, and the inverse proposition of Cramer rule is also proved to be true. Keywords System of Linear Equations, Cramer Rule, The Inverse Proposition of Cramer Rule, The Properties of Determinant 一个关于克拉默法则及其逆命题的注记 杜志斌 肇庆学院数学与统计学院，广东 肇庆 收稿日期：2017年2月26 日；录用日期：2017年3月18 日；发布日期：2017年3月21 日 摘 要 解线性方程组是高等代数和线性代数中的一个重要内容。克拉默(Cramer)法则运用了行列式来刻画线性 方程组解的存在性和唯一性，它适用于方程个数与未知量个数相等的线性方程组，具有显著的理论价值。 本文将利用行列式的性质给出克拉默法则的另一种证明，并证明克拉默法则的逆命题也是正确的。 文章引用: 杜志斌. 一个关于克拉默法则及其逆命题的注记[J]. 应用数学进展, 2017, 6(2): 127-132. /10.12677/aam.2017.62014 杜志斌 关键词 线性方程组，克拉默(Cramer)法则，克拉默(Cramer)法则的逆命题，行列式性质 Copyright © 2017 by author and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Open Access 1. 引言 线