克莱姆法则的又一证法

Another Proof method of Cramer's Rule

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。

In linear algebra teaching, Cramer's rule is an important theorem. Cramer's rule has a lot of applications. In the introduction of determinant, most textbooks derive Cramer's rule from the solution of linear equations followed by the definition of the determinant. Cramer's rule is applied in so many calculation methods of higher algebra, spatial analytic geometry, and calculus. There are also many proof method of Cramer's rule. This thesis gives a new proof method as bordered determinant which proves to be very simple.