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单选题 如果( ),则矩阵
相似
A. 
B. 具有相同的特征值
C. 
D. 
阶矩阵有相同的特征值且个特征值各不相同
学科：线性代数
时间：2025-10-31 11:36:48
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题目1单选题
下列排列为奇排列的是(A. <img src="https://tihai-oss-cloud.itihey.com/img/d00e29ce6ddce9f6e79450edf5fa0fa4.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/ee9ad70bcdf9bf64f9ea1c37ea1889cb.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/f28fbbd80ad321d4b79650381f6256ba.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/09edcca2b38bb1ad48bf88f2db45cfe9.png">
题目2单选题
<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">阶矩阵<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">可逆,则下列命题不正确的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/2c0cdb6a6b1bb4a0ea8905f2fd80a822.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的行向量中存在零向量C. <img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的列秩为<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">D. 当<img src="https://tihai-oss-cloud.itihey.com/img/803e47c8f92f13fafbcdb27a6cc00520.png">时,<img src="https://tihai-oss-cloud.itihey.com/img/7a7155ee8868522879524af1a1aecfaf.png">,其中<img src="https://tihai-oss-cloud.itihey.com/img/065103d8f767d7f3310552c15543693c.png">
题目3单选题
向量<img src="https://tihai-oss-cloud.itihey.com/img/203fd730f450a65da07b49715e01d3f1.png">线性无关,则下列结论不成立的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/203fd730f450a65da07b49715e01d3f1.png">均不是零向量B. <img src="https://tihai-oss-cloud.itihey.com/img/203fd730f450a65da07b49715e01d3f1.png">中任意两个向量都不成比例C. <img src="https://tihai-oss-cloud.itihey.com/img/203fd730f450a65da07b49715e01d3f1.png">任一部分组线性无关D. <img src="https://tihai-oss-cloud.itihey.com/img/203fd730f450a65da07b49715e01d3f1.png">中存在一个向量可由其余<img src="https://tihai-oss-cloud.itihey.com/img/3c84ef78cb1efa8fe934ecf9acd4d2de.png">个向量线性表示
题目4单选题
矩阵<img src="https://tihai-oss-cloud.itihey.com/img/2a4f62061102c759efa88f360a6d4697.png">的逆矩阵为()A. <img src="https://tihai-oss-cloud.itihey.com/img/3384834787115d76c47259e0468451eb.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/54b8b7b5007d4ce980dae4e3d833f8d4.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/ca09d7719acc7bc294778595de628e56.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/bdca136cff6302eee8c418ebc0ee28e3.png">
题目5单选题
矩阵<img src="https://tihai-oss-cloud.itihey.com/img/a8dc138c3e3fe1885559bc6afa46be87.png">与下列哪个矩阵不相似的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/c2c99076fcf4e84e57254f0cb2fc1706.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/57f2512b3df677d686b8eb6d147bb107.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/a3a5b10190a911b72b6f96b9065ab264.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/cfffe4e5689eca0c8aef77486c2f0cfe.png">
题目6单选题
设<img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">是两个相似的<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">阶矩阵,则下列结论错误的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/a85c2410850e6b7c309035296de2fc50.png">B. 存在对角阵<img src="https://tihai-oss-cloud.itihey.com/img/655cd93c307406537175fb86e19c9d57.png">,使<img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">都相似于<img src="https://tihai-oss-cloud.itihey.com/img/655cd93c307406537175fb86e19c9d57.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/db81dfa06b5d585aa568ac8e184b570f.png">D. 存在非奇异矩阵<img src="https://tihai-oss-cloud.itihey.com/img/6806b54c6f9fbde684000e3335767b9d.png">,使<img src="https://tihai-oss-cloud.itihey.com/img/552f6a2daae8e47b64ec00b6e4bd43a6.png">
题目7单选题
<img src="https://tihai-oss-cloud.itihey.com/img/24506d26963eb6cb04a89dd28a51d259.png">都是<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">阶矩阵<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">,<img src="https://tihai-oss-cloud.itihey.com/img/52a2ed1521d193d96b42d3cc7074de50.png">且<img src="https://tihai-oss-cloud.itihey.com/img/598b550b8cd45db19b147e2f69893a8b.png">分别是对应于<img src="https://tihai-oss-cloud.itihey.com/img/24506d26963eb6cb04a89dd28a51d259.png">的特征向量,当( )时,<img src="https://tihai-oss-cloud.itihey.com/img/1c6431a7332296e174560762e9c153cb.png">必是<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">的特征向量A. <img src="https://tihai-oss-cloud.itihey.com/img/5f99aafa9efa1846c24a6fa2449380ca.png">且<img src="https://tihai-oss-cloud.itihey.com/img/5100aa5c4600ee28954049b93ea5545a.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/879414ab3094a96bec7635d52b785dcd.png">且<img src="https://tihai-oss-cloud.itihey.com/img/6faf69198fc581c2de6b5984227a2ea9.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/879414ab3094a96bec7635d52b785dcd.png">且<img src="https://tihai-oss-cloud.itihey.com/img/5100aa5c4600ee28954049b93ea5545a.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/ea693c7484a892ffb8f6582fe8c6b3d4.png">
题目8单选题
如果( ),则矩阵<img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">相似A. <img src="https://tihai-oss-cloud.itihey.com/img/a85c2410850e6b7c309035296de2fc50.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">具有相同的特征值C. <img src="https://tihai-oss-cloud.itihey.com/img/d9b035fc7642bfb6026c4491fd186c84.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">阶矩阵<img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">有相同的特征值且<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">个特征值各不相同
题目9单选题
若矩阵可逆,则以下选项中正确的是()A. <img src="https://tihai-oss-cloud.itihey.com/img/0d2a5074e00b1640fc146ce9f1102b55.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/205b6d9fb4569fe3c8266128564cb3a6.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/d1900043b288d36629ee3a4e08827de6.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/d44d0d5dc1886fa0176684c628222ded.png">
题目10单选题
设n阶方阵<img src="https://tihai-oss-cloud.itihey.com/img/a713b51ea3a6b4aaac47146015fc102a.png">,则下列结论一定正确的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/f561c40ef710a8abb5203a10fdde2856.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/acb12c64aeb136f60512fa3ed8fa73c5.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/fe35237d14abce2be3687212b4823e8c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/bfcabd000a427e02dcb40f7dda751a51.png">
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