初等变换求矩阵的秩在线性代数中的应用

Application of Calculating Matrix Rank with Elementary Transformation in Linear Algebra

分析了初等变换方法求矩阵的秩、利用初等变换求矩阵的秩与高斯消元法解线性方程组,向量组的线性表示,向量组的线性相关性的相通性原理,将初等变换求秩应用在以上方面,既解决了三个问题的求解判断,更将知识融会贯通,紧密联系在一起,为以后相关知识的学习奠定基础。

This paper analyzes the method of calculating matrix rank with elementary transformation, utilizes the method and Gauss elimination to solve linear equations, analyzes the linear representation of vector group, the similarity principle of the linear relevance of vector group, and applies the method of calculating matrix rank with elementary transformation to the above three aspects. It can not only settle the solving and judgment of the three problems, but also integrate the learned knowledge, so as to lay a foundation for future learning.