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证明若向量组有不止一个极大线性无关组是,不同线性无关组中的向量个数一样多
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亲亲,非常荣幸为您解答![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
假设存在一个向量组$V$,它有两个不同的极大线性无关组,分别为$B=\{v_1,v_2,\cdots,v_r\}$和$C=\{u_1,u_2,\cdots,u_s\}$,其中$r
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
咨询记录 · 回答于2023-05-05
证明若向量组有不止一个极大线性无关组是,不同线性无关组中的向量个数一样多
亲亲,非常荣幸为您解答![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
假设存在一个向量组$V$,它有两个不同的极大线性无关组,分别为$B=\{v_1,v_2,\cdots,v_r\}$和$C=\{u_1,u_2,\cdots,u_s\}$,其中$r
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_02.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_207.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)
![](https://s.bdstatic.com/common/openjs/emoticon/img/face_246.png)