基于教学实践的矩阵秩教学设计研究  

Study on the Teaching Design of the Rank of Matrix Based on Teaching Practice

作　　者：张会平[1] Zhang Huiping(School of Mathematics, Renmin University of China, Beijing 100872, China)

机构地区：[1]中国人民大学数学学院,北京100872

出　　处：《黑龙江科学》2022年第13期123-125,共3页Heilongjiang Science

基　　金：国家自然科学基金项目,项目名称:多复变中与群作用相关问题的研究(11671399)。

摘　　要：基于教学实践,对矩阵的秩进行教学设计,给出了矩阵的秩在实际教学中的处理办法。介绍了矩阵的行秩、列秩、秩的概念,证明初等变换不改变矩阵的行秩与列秩、矩阵的行秩与矩阵的列秩相等、矩阵的秩等于矩阵的列秩,给出矩阵的秩的求法及向量组的极大无关组的求法,以期降低学习难度,从多角度解决实际问题。Based on teaching practice,the study designs the teaching of the rank of matrix;proposes the method of the rank of matrix in practical teaching;introduces the concept of column rank,row rank and the rank of matrix;proves that column rank and row rank are not changed in elementary transformation,row rank equals to column rank in the matrix,the rank of matrix equals to the column rank of matrix;provides the solution of the rank of matrix and maximal linearly independent vector quantity,to decrease learning difficulties,and solve practical problems from multi-angles.

关 键 词：教学实践 矩阵的秩 教学设计 

分 类 号：O151.2[理学—数学]