齐次线性方程组的一种简捷的公式化解法

A simple formulated solution of homogeneous linear equations

n元齐次线性方程组当其矩阵的秩小于 n时有非零解.要求出这个非零解,通常是将矩阵进行初等变换而得到.但对矩阵的秩是一个 n-1的方程组,却有一个和克莱姆法则一样的简捷的公式化解法.这一解法对三元齐次线性方程组来说特别方便.

Homogeneous linear equations of n-variables have the non-zero solutions when the rank of its matrix is less than n. To get this solution, the matrix can be proceeding elementary operation. But to the equation whose rank of matrix is n-1, there is a formulated solution as simple as the Cramer Law. This solution is very convenience for the homogeneous linear equations of 3-variables.