线性方程组解的应用

Application of Solutions for System of Linear Equations

齐次线性方程组有非零解的条件定理在代数,解析几何上有重要的应用.用齐次线性方程组有非零解的充要条件定理可以解决初等数学中的某些问题.方程组的解结构和相应的行向量组或列向量组的相关性分析是该理论的难点,齐次方程组有非零解与对应的行向量组或列向量组线性相关性有对应关系,非齐次方程组有解和向量的表示有一种对应关系,要学会灵活的应用这些关系来分析问题.

In this paper the conditional theorem of linear homogenous equqtion system with non - zero solution and its application in algebra and analytical geometry are discussed. The principle of the necessary and sufficient condition applied of the system of homogeneous linear equations is applied for the solution of some problems in elementary mathematics. The difficult points of this theory are to analyze the structure of solution of the system of equations and vector set and row vector set. That system of homogeneous equations with non - zero solutions is related with vector set and row vector set. These relations to analyze the problems should be flexibly used.