线性方程组解法新探

Discussion of linear equations solution

通过引入拓展矩阵和转解运算,根据分块矩阵理论及矩阵初等变换,分别用2种方法求出了当系数矩阵的秩等于增广矩阵的秩且小于未知数的个数时,非齐次线性方程组所对应的齐次线性方程组的基础解系和非齐次线性方程的特解.从而直接从矩阵中求出线性方程组的通解,给出了求解线性方程组的一种思路.

Through the introduction of expansion matrix and transfer matrix operation, and according to block matrix theory and elemantary transformation matrix, the system of basic solutions of homogeneous linear equations and the special solution of non-homogeneous linear equations are obtained by two methods,when the rank of coefficient matrix is equal to the rank of augmented matrix and less than unknown numbers. Thus the general solution of linear equations is directly drived from matrix,and a idea for solving linear equations is given.