探讨线性方程组求解问题  

Exploring the Problem of Solving Systems of Linear Equations

作　　者：林清华 LIN Qinghua(Minjiang Teachers College,Fuzhou,Fujian Proivince,350000 China)

机构地区：[1]闽江师范高等专科学校,福建福州350000

出　　处：《科技资讯》2024年第13期232-235,共4页Science & Technology Information

摘　　要：对于线性方程组,只有在方程的个数等于未知量的个数,系数行列式不等于零的情况下,才可以使用克莱姆法则求得,也可以使用逆矩阵法求得。而对于一般的线性方程组,如何判定它是否有解、解是否唯一,以及在解不唯一的情况下,又该如何求出它的解。这个问题的解决,对理论和实际都具有十分重要的意义。以下以矩阵为工具,探求一般线性方程组解的情况和解的问题。A system of linear equations can be solved by using Cramer's Rule only if the number of equations is equal to the number of unknowns and the determinant of the coefficients is not equal to zero,and it can also be solved by using the inverse matrix method.And for a general system of linear equations,how to determine whether it has a solution,whether the solution is unique,and how to find its solution if the solution is not unique.The solution of this problem is of great importance for both theory and practice.The following matrix is used as a tool to explore the solution of general linear equations.

关 键 词：线性方程组 系数矩阵 基础解析 通解 

分 类 号：G642[文化科学—高等教育学]