用矩阵变换法解二元一次不定方程

Solving Binary Indeterminate Equation by Matrix Transformation

解二元一次不定方程的关键是求它的特解,文章将二元一次不定方程与矩阵联系起来,运用矩阵的初等变换求得未知项系数的最大公约数,以判断二元一次不定方程解的存在性,若解存在可直接给出方程的一组特解,进而求出方程的通解.

The key for solving binary indeterminate equation is to obtain its particular solution, this paper combines bi- nary indeterminate equation with matrix, use the matrix transformation to obtain the greatest common factor of the unknown coefficient to judge the existence of the solutions for binary indeterminate equation. If the solution exists, then we can get the special solution, thence the common solution is obtained.