线性方程组解的结构探讨

A simple exploration on structure of solutions of system of linear equations

利用分块矩阵的性质来研究一般线性方程组解的结构,给出了一般线性方程组AX=b的解存在的充分必要条件为-A21A1-11b1┇br+br+1┇bm=0.其中,R(A)=R(A11)=r,A11为A的r×r阶子块,A21为A的(n-r)×r阶子块.同时在方程组有解时给出了此线性方程组的通解.

The stucture of solutions of the system of linear equations by the properties of block matrices was discussed. The sufficient and necessary condition that the solutons of the system of linear equations AX = b.-A21A11^-1{b1…br}＋{br＋1…bm}=0 where R（A） = R（A11 ） = r,A11 is a r × r subblock of matrix A ,A21 is a （n - r） × r subblock of matrix A. And the general solution of the system of linear equations was present if there exist some solutions in the system.