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多选题 以下结论正确的是( )
A. 对
矩阵
,有
B. 
C. 对于
阶矩阵,矩阵为满秩矩阵的充分必要条件是
D. 对于阶矩阵,矩阵为降秩矩阵的充分必要条件是
学科：23-24(2)线性代数
时间：2024-03-31 08:55:40
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题目1多选题
以下叙述正确的是( )A. 若<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">中有一个<img src="https://tihai-oss-cloud.itihey.com/img/3976cccc520a3071d27c821c613bb6ea.png">阶子式不为零,则<img src="https://tihai-oss-cloud.itihey.com/img/a60532ae11a1ee987074f4f4928e967e.png">B. 若<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">中有一个<img src="https://tihai-oss-cloud.itihey.com/img/3976cccc520a3071d27c821c613bb6ea.png">阶子式不为零,则<img src="https://tihai-oss-cloud.itihey.com/img/e612c89a3a0515719a8466d9ffa8915a.png">C. 若<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">中所有<img src="https://tihai-oss-cloud.itihey.com/img/3976cccc520a3071d27c821c613bb6ea.png">阶子式全为零,则<img src="https://tihai-oss-cloud.itihey.com/img/ecb57841904002feaf1d3cfb478c3358.png">D. 非零矩阵的秩至少等于1
题目2多选题
以下结论正确的是( )A. 对<img src="https://tihai-oss-cloud.itihey.com/img/f09fb3eec5bf1c6d60aa058c9c15eb84.png">矩阵<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">,有<img src="https://tihai-oss-cloud.itihey.com/img/b68ff8e0b598c72110afbe83084dc735.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/82869f6433e9ce7166fac8714cf65f80.png">C. 对于<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">,矩阵<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">为满秩矩阵的充分必要条件是<img src="https://tihai-oss-cloud.itihey.com/img/eff78099e3774a245b97ed1f1609a042.png">D. 对于<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">,矩阵<img src="https://tihai-oss-cloud.itihey.com/img/54f4567d5d1aa85ddf2c5f3ce75ecf98.png">为降秩矩阵的充分必要条件是<img src="https://tihai-oss-cloud.itihey.com/img/bfbce8559c53596d054cb9c2872212e6.png">
题目3单选题
以下性质错误的是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/6733780312afc9a8ada1ac5b2e33bdc4.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/33fadf4abf7519ccd91910b359cbde0c.png">C. 若<img src="https://tihai-oss-cloud.itihey.com/img/65014a873c58e7a18dc82bb3b55c3a8e.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/5039fb54c11ab489bc042a316748bc00.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/891b9544c45cb9a25981f5abcccc71e5.png">E. <img src="https://tihai-oss-cloud.itihey.com/img/9618cd0499a3ec600a54de33bdc82310.png">F. 若<img src="https://tihai-oss-cloud.itihey.com/img/13e253d8a90531193b96985e127d71c0.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/1a26e776c470534a474339adb7466f88.png">
题目4单选题
<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">元线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/5096db8c37f7635db9f93f4f320db365.png">,且<img src="https://tihai-oss-cloud.itihey.com/img/267943ee2c272bae4f2d9c7c5693e693.png">,则方程组<img src="https://tihai-oss-cloud.itihey.com/img/5096db8c37f7635db9f93f4f320db365.png">( )A. 有唯一解B. 有无穷多个解C. 无解D. 无法确定
题目5单选题
<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">元齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/fa09c561b39111ddfb5edd26292138cf.png">,且<img src="https://tihai-oss-cloud.itihey.com/img/267943ee2c272bae4f2d9c7c5693e693.png">,则方程组<img src="https://tihai-oss-cloud.itihey.com/img/fa09c561b39111ddfb5edd26292138cf.png">( )A. 只有零解B. 有非零解C. 无解D. 无法确定
题目6单选题
4元线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/2b6fa33b3b42780fe060bdd4953c0ac3.png"> ( )A. 只有零解B. 有非零解C. 无解D. 无法确定
题目7单选题
问<img src="https://tihai-oss-cloud.itihey.com/img/1918d65b5b15ac6ae048979607ad9c8a.png">取何值时,线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/586598158f1e26df64f7d57f3cfa6b88.png"> 有唯一解A. <img src="https://tihai-oss-cloud.itihey.com/img/99c9e7c7c53c85d04104e37eb8c9a0c1.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/2ae18896bac09bf4cad6c8880f5b06a8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/a44afe809b3210670abdce748bdafbeb.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/361d3210eff32b54f0bc638637ab902f.png">
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