在线性代数教学中,克莱姆法则是一个重要定理。克莱姆法则有大量的应用,多数课本在讲行列式的引入都是从解线性方程组导出克莱姆法则,再给出行列式的定义。克莱姆法则在高等代数、空间解析几何、微积分、计算方法都有大量的应用。克莱姆法则的证明也有很多种方法,本文给出一种新的证明方法,用加边行列式的方法来证明,证明比较简单。 Klein’s law is an important theorem in linear algebra teaching. There are many applications of Cramer’s Law. Most textbooks are introducing determinants of Cramer’s law from linear equations, and then we give the definition of determinants. Cramer’s law has many applications in higher algebra, space analytic geometry, calculus and calculation methods. There are many ways to prove the Clem’s law. In this paper, we present a new method of proof, proved by the addition of determinant, which is proved to be relatively simple.