克拉默法则的一个简单证明及其推广

A Simple Proof of Cramer Rule and Its Promotion

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。

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.