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单选题 下列说法不正确的是【 】
A. 如果
个向量
线性无关,则加入
个向量
后,仍然线性无关
B. 如果个向量线性无关,则在每个向量中增加个分量后所得向量组仍然线性无关
C. 如果个向量线性相关,则加入个向量后,仍然线性相关
D. 如果个向量线性相关,则在每个向量中去掉个分量后所得向量组仍然线性相关
学科：线性代数
时间：2024-05-17 17:06:58
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题目1单选题
<img src="https://tihai-oss-cloud.itihey.com/img/5fec55d3afca0775ec3f88202706a2cc.png"> 维向量组 <img src="https://tihai-oss-cloud.itihey.com/img/d833a0c2b0bce2c523c995ca57955366.png">(<img src="https://tihai-oss-cloud.itihey.com/img/e4b88f9a7bad700a53dd7c17cce42019.png">)线性无关的充要条件是【 】A. <img src="https://tihai-oss-cloud.itihey.com/img/d833a0c2b0bce2c523c995ca57955366.png">中任意两个向量都线性无关B. <img src="https://tihai-oss-cloud.itihey.com/img/d833a0c2b0bce2c523c995ca57955366.png">中存在一个向量不能用其余向量线性表示C. <img src="https://tihai-oss-cloud.itihey.com/img/d833a0c2b0bce2c523c995ca57955366.png">中任一个向量都不能用其余向量线性表示D. <img src="https://tihai-oss-cloud.itihey.com/img/d833a0c2b0bce2c523c995ca57955366.png">中不含零向量
题目2单选题
下列命题中正确的是【 】A. 任意<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">个<img src="https://tihai-oss-cloud.itihey.com/img/18e3a55098294159eb8c770c3d1d6ba5.png">维向量线性相关B. 任意<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">个<img src="https://tihai-oss-cloud.itihey.com/img/18e3a55098294159eb8c770c3d1d6ba5.png">维向量线性无关C. 任意<img src="https://tihai-oss-cloud.itihey.com/img/18e3a55098294159eb8c770c3d1d6ba5.png">个<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png"> 维向量线性相关D. 任意<img src="https://tihai-oss-cloud.itihey.com/img/18e3a55098294159eb8c770c3d1d6ba5.png">个<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png"> 维向量线性无关
题目3单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">为<img src="https://tihai-oss-cloud.itihey.com/img/5e07d4d8f85c675398c0405005c31890.png">矩阵,齐次方程组<img src="https://tihai-oss-cloud.itihey.com/img/bcc0cabafdb7e9eab6eb3b7c1d3083c1.png">仅有零解的充要条件是【 】A. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的列向量线性无关B. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的列向量线性相关C. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的行向量线性无关D. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的行向量线性相关
题目4单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/4a64e4a93f506b9a0be5729cd7387dc3.png">是<img src="https://tihai-oss-cloud.itihey.com/img/5fec55d3afca0775ec3f88202706a2cc.png">个<img src="https://tihai-oss-cloud.itihey.com/img/3a04239722efc9c12225ecd25b9ca212.png">维向量,且<img src="https://tihai-oss-cloud.itihey.com/img/ce49a19e9f86a5da86aad49fbcc7bba5.png">, 则此向量组<img src="https://tihai-oss-cloud.itihey.com/img/4a64e4a93f506b9a0be5729cd7387dc3.png">必定【 】A. 线性相关B. 线性无关C. 含有零向量D. 有两个向量相等
题目5单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">为<img src="https://tihai-oss-cloud.itihey.com/img/a1be902db3b2577725e1b19c37977d16.png">阶矩阵,如果<img src="https://tihai-oss-cloud.itihey.com/img/1b8ea1169a0831b24ef8092f161fd305.png"> , 则 【 】A. <img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的任意一个行(列)向量都是其余行(列)向量的线性组合B. <img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的各行向量中至少有一个为零向量C. <img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的行(列)向量组中必有一个行(列)向量是其余各行(列)向量的线性组合D. <img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的行(列)向量组中必有两个行(列)向量对应元素成比例
题目6单选题
已知向量组<img src="https://tihai-oss-cloud.itihey.com/img/6fd9d689de21f7141be9d439478bd86c.png">线性无关则向量组【 】A. <img src="https://tihai-oss-cloud.itihey.com/img/63a174e756ea62f175722f535ac403cb.png">线性无关B. <img src="https://tihai-oss-cloud.itihey.com/img/b214e40ac663fa5178f4e7de40c79a7f.png">线性无关C. <img src="https://tihai-oss-cloud.itihey.com/img/a7a163feb31913872289579d26aa895c.png">线性无关D. <img src="https://tihai-oss-cloud.itihey.com/img/ef2d3aade0a7f1433f99c722513b04b3.png">线性无关
题目7单选题
下列说法不正确的是【 】A. 如果<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个向量<img src="https://tihai-oss-cloud.itihey.com/img/33daf899431b218434c86cfc52ab3cde.png">线性无关,则加入<img src="https://tihai-oss-cloud.itihey.com/img/69ae27cdc4162ffd91a6adcaf18ed10d.png">个向量<img src="https://tihai-oss-cloud.itihey.com/img/4cf41092033fca20a133069f4515a98b.png">后,仍然线性无关B. 如果<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个向量<img src="https://tihai-oss-cloud.itihey.com/img/33daf899431b218434c86cfc52ab3cde.png">线性无关,则在每个向量中增加<img src="https://tihai-oss-cloud.itihey.com/img/69ae27cdc4162ffd91a6adcaf18ed10d.png">个分量后所得向量组仍然线性无关C. 如果<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个向量<img src="https://tihai-oss-cloud.itihey.com/img/33daf899431b218434c86cfc52ab3cde.png">线性相关,则加入<img src="https://tihai-oss-cloud.itihey.com/img/69ae27cdc4162ffd91a6adcaf18ed10d.png">个向量后,仍然线性相关D. 如果<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个向量<img src="https://tihai-oss-cloud.itihey.com/img/33daf899431b218434c86cfc52ab3cde.png">线性相关,则在每个向量中去掉<img src="https://tihai-oss-cloud.itihey.com/img/69ae27cdc4162ffd91a6adcaf18ed10d.png">个分量后所得向量组仍然线性相关
题目8单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/5fec55d3afca0775ec3f88202706a2cc.png">阶方阵<img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的秩<img src="https://tihai-oss-cloud.itihey.com/img/9bbd385f3f30969f5c7946ee8165b1dd.png">,则在<img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的<img src="https://tihai-oss-cloud.itihey.com/img/5fec55d3afca0775ec3f88202706a2cc.png">个行向量中【 】A. 任意<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个行向量均可构成极大无关组B. 必有<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个行向量线性无关C. 任意<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个行向量均线性无关D. 任一行向量均可由其他<img src="https://tihai-oss-cloud.itihey.com/img/5b8063ce4307a42d73f40513a3f6f4e2.png">个行向量线性表示
题目9单选题
设方阵<img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">的行列式<img src="https://tihai-oss-cloud.itihey.com/img/16f79c0cd6b6ca65859c14436923937e.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/24e546db3c15bf8e0f0be3424361423e.png">中 【 】A. 必有一行(列)元素为零B. 必有两行(列)成比例C. 必有一行向量是其余行(列)向量的线性组合D. 任一行向量是其余行(列)向量的线性组合
题目10单选题
设向量组<img src="https://tihai-oss-cloud.itihey.com/img/2eea837c8d5c5eeb94ed26951ef959d0.png"> 线性相关,则【 】由<img src="https://tihai-oss-cloud.itihey.com/img/092721abe8d89023d3fecf2e4946a03e.png">线性表出A. 每个<img src="https://tihai-oss-cloud.itihey.com/img/4690c185b8a9233346d5edf4d02cb8a9.png">都能B. 每个<img src="https://tihai-oss-cloud.itihey.com/img/4690c185b8a9233346d5edf4d02cb8a9.png">都不能C. 某一个<img src="https://tihai-oss-cloud.itihey.com/img/4690c185b8a9233346d5edf4d02cb8a9.png">不能D. 有一个<img src="https://tihai-oss-cloud.itihey.com/img/4690c185b8a9233346d5edf4d02cb8a9.png">能
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