线性方程组求解及应用

Solution of System of Linear Equations and Its Applications

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.