摘要
本文通过几个反例说明了在求向量组的极大无关组时，以往普遍使用的以向量为行向量作矩阵，再对矩阵作初等行变换的方法是不完善的，甚至会导致错误的结果。构造并证明了线性无关向量组的一个充分条件，给出了求极大无关组的一个简单可行的新方法。
The article by several opposite examples illustrated the former method of finding vector group's maximum linearly independent vector group is imperfect, sometimes even lead to wrong results. The method is that make use of row vector as matrix and then change matrix by performing elementary row operation. The article constructed and proved the one sufficient condition of linearly independent vector group, also a new, simple, practical method to find maximum linearly independent vector group.
关键词
极大无关组
初等行变换
矩阵
向量
线性相关
maximum linearly independent vector group
elementary row operation
matrix
vector
linearly independent
linearly dependent
