克莱姆法则的推广和完善

The Extension and Refinement of Cramer Rule

克莱姆法则是线性代数中的重要内容,但克莱姆法则只解决了当线性方程组系数行列式不等于零时,线性方程组的解的存在性和唯一性问题.当系数行列式等于零时,线性方程组无解或者有无穷多解.什么条件下线性方程组无解?什么条件下线性方程组有无穷解?当线性方程组有无穷解时,这无穷解的通解的结构是什么?克莱姆法则没有给出答案.所以需要推广和完善,这在线性方程组的解的结构理论上是很有用的.

Cramer rule is an important content in linear algebra. But Cramer rule only solved the linear system of equations de- terminant of coefficient is not equal to zero, the system of linear equations solution existence and uniqueness problem. When the determinant of coefficient is equal to zero, system of linear equations has no solution or has an infinite number of solutions. What conditions linear equations has no solution？ What conditions linear equations with infinite solutions？ When solutions of linear e- quations with infinite time, what is the structure of general solutions of infinite solutions？ Cramer did not give an answer. So it needs to promote and perfect, and it is very useful in the system of linear equations solution structure theory.