关于极大线性无关组和线性空间中基的扩充问题的讨论

Discussion on the Expansion of Maximum Linear Independent Groups and Bases in Vector Space

线性空间是线性代数中一个重要的研究对象,基与维数又能决定一个线性空间的结构,因此在已知的线性空间中找到满足要求的基是一个值得探讨的问题。本文根据线性空间中的扩充基定理,讨论了由给定线性无关的向量组扩充成一个极大线性无关组,以及在线性空间扩充成一组基的一般解法,旨在加深学生对极大线性无关组以及线性空间中基的理解。

Linear space is an important research object in linear algebra, and the basis and dimension can determine the structure of a linear space. So it is a worthwhile problem to find the required basis in a linear space. In this paper, according to the expansion basis theorem in the linear space, we discuss how to find the maximum linear independent vector group or the basis for a given linear independent list in the linear space. It can promote the students’ understanding of the maximum linear independent vector group and the bases in the linear space.