线性方程组求解及应用  

Solution of System of Linear Equations and Its Applications

作　　者：石擎天 黄坤阳 SHI Qing-tian;HUANG Kun-yang(Quanzhou Normal University,School of Mathematics and computation Science,Quanzhou,Fujian 362000,China;Fujian Provincial Key Laboratory of Data Intensive Computing,Quanzhou,Fujian 362000,China)

机构地区：[1]泉州师范学院,数学与计算机科学学院,福建泉州362000 [2]智能计算与信息处理福建省高校重点实验室,福建泉州362000

出　　处：《教育教学论坛》2020年第12期325-327,共3页Education And Teaching Forum

基　　金：泉州师范学院科研计划项目(H19009);福建省中青年教师教育科研项目(JAT190508)

摘　　要：文章首先介绍了用克拉默法则求解一类线性方程组(方程的个数与未知量个数相同且系数行列式不为零),由此提出对于一般的线性方程组如何求解问题.从而引出用矩阵的秩来判定线性方程组的解的结构以及用初等变换来求线性方程组的通解.最后应用线性方程组的求解问题对矩阵方程和向量组的线性相关性进行分析.In this paper,we first introduce the Cramer's rule to solve a kind of system of linear equations,which has the same numbers of equations and variables and its determinant of the coefficients is not zero.Thus we post a question that how to solve every system of linear equations.Hence,the rank of matrix is used to determine the structure of solutions of system of linear equations and elementary transformation is used to deduce its general solutions.Last,two kinds of applications of solutions of system of linear equations are discussed on the matrix equation and linear correlation of vectors.

关 键 词：线性方程组 克拉默法则 初等变换 矩阵方程 

分 类 号：G642.41[文化科学—高等教育学]