一个关于克拉默法则及其逆命题的注记

Abstract

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。 Solving the systems of linear equations plays an important role in higher algebra and linear algebra. 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 determinant, and the inverse proposition of Cramer rule is also proved to be true.