第三章　向量空间

单选

设向量组，，线性无关，则以下向量组中线性无关的是（）

A <img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" /> B <img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />-<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" /> C <img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+2<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" /> D <img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257919373521.png" width="24" height="29" />+<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161257920171221.png" width="22" height="30" />一<img src="https://www.beizhujiaoyu.com/uploads/202208/161257918767671.png" width="20" height="29" />

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单选

设向量组(I)：，，…，的秩为r，则必有（）

A (I)中任意r个向量必线性无关 B (I)中任意r-1个向量必线性无关 C (I)中任意r+1个向量必线性相关 D (I)中线性相关向量的个数必大于r

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单选

向量组，…，(s≥2)的秩为零的充要条件是

A <img src="https://www.beizhujiaoyu.com/uploads/202208/161258348031981.png" width="47" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/161258347435661.png" width="22" height="30" />全是零向量 B <img src="https://www.beizhujiaoyu.com/uploads/202208/161258348657111.png" width="47" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/161258347435661.png" width="22" height="30" />中没有线性相关的部分组 C <img src="https://www.beizhujiaoyu.com/uploads/202208/161258348657111.png" width="47" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/161258347435661.png" width="22" height="30" />中可以有非零向量 D <img src="https://www.beizhujiaoyu.com/uploads/202208/161258348657111.png" width="47" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/161258347435661.png" width="22" height="30" />可以全是非零向量

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单选

n维向量组，，…，(s≥2)线性相关充要条件（）

A <img src="https://www.beizhujiaoyu.com/uploads/202208/161266914012561.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161266914543171.png" width="24" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/16126691514171.png" width="22" height="30" />中至少有两个向量成比例 B <img src="https://www.beizhujiaoyu.com/uploads/202208/161266914012561.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161266914543171.png" width="24" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/16126691514171.png" width="22" height="30" />中至少有一个是零向量 C <img src="https://www.beizhujiaoyu.com/uploads/202208/161266914012561.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161266914543171.png" width="24" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/16126691514171.png" width="22" height="30" />中至少有一个向量可以由其余向量线性表出 D <img src="https://www.beizhujiaoyu.com/uploads/202208/161266914012561.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161266914543171.png" width="24" height="29" />，…，<img src="https://www.beizhujiaoyu.com/uploads/202208/16126691514171.png" width="22" height="30" />中每一个向量都可以由其余向量线性表出

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单选

若向量组=(1，t+1，0)，=(1，2，0)，=(0，0，t一1)线性无关，则实数t（）

A ≠0 B ≠1 C ≠2 D ≠3

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单选

已知向量组=(1，-1，1)，=(-1，1，1)，=(1，1，-1)，此向量组的秩为（）

A 0 B 1 C 2 D 3

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单选

设向量=()，=()，β=(，，，)，β=(,)，下列命题中正确的是（）

A 若<img src="https://www.beizhujiaoyu.com/uploads/202208/161267093750981.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161267099565881.png" width="24" height="29" />线性无关，则必有β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267113735681.png" width="10" height="29" />，β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267114450411.png" width="14" height="29" />线性无关 B 若<img src="https://www.beizhujiaoyu.com/uploads/202208/161267093750981.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161267099565881.png" width="24" height="29" />线性相关，则必有β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267113735681.png" width="10" height="29" />，β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267114450411.png" width="14" height="29" />线性相关 C 若β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267113735681.png" width="10" height="29" />，β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267114450411.png" width="14" height="29" />线性相关，则必有<img src="https://www.beizhujiaoyu.com/uploads/202208/161267093750981.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161267099565881.png" width="24" height="29" />线性无关 D 若β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267113735681.png" width="10" height="29" />，β<img src="https://www.beizhujiaoyu.com/uploads/202208/161267114450411.png" width="14" height="29" />线性无关，则必有<img src="https://www.beizhujiaoyu.com/uploads/202208/161267093750981.png" width="20" height="29" />，<img src="https://www.beizhujiaoyu.com/uploads/202208/161267099565881.png" width="24" height="29" />线性无关

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单选

下列命题中错误的是

A 一个非零向量线性无关 B 任意一个含零向量的向量组线性相关 C 由4个三维向量组成的向量组线性相关 D 由3个四维向量组成的向量组线性无关

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单选

设A为m×n矩阵，则n元齐次线性方程组Ax=0存在非零解的充要条件为（）

A A的列向量线性无关 B A的行向量线性无关 C A的列向量线性相关 D A的行向量线性相关<p> </p><p>

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分析

填空题:若，，线性无关，，，线性相关，则向量组，2，3的极大无关组是_______．

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