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单选题设为 4 维列向量组, 且.已知线性方程组的通解为则向量组的一个极大线性无关组为

A.

B.

C.

D.

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学科：默认课程

时间：2025-12-31 23:22:33

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解方程组<img src="https://tihai-oss-cloud.itihey.com/img/3e7faa12b61fca2df0ef10cf154ae789.png">时,对增广矩阵(<img src="https://tihai-oss-cloud.itihey.com/img/f41d74b871b0ec296c21cc4658ec5dbe.png">)施行的初等变换<img src="https://tihai-oss-cloud.itihey.com/img/84d8239b247391367cf1177f287922c3.png">

A. 只能进行初等行变换B. 允许进行某种初等列变换C. 既可进行初等行变换也可进行初等列变换D. 只允许进行某一种初等列变换

设<img src="https://tihai-oss-cloud.itihey.com/img/343c4533a57827c06afb20cb3bb85ab9.png">是非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/096ac92b2b262969bf4218c29a5bbbd5.png">的两个不同的解,<img src="https://tihai-oss-cloud.itihey.com/img/ca3d9ef6b27802f2b4ca42ba998db4ae.png">是对应的齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/7300862129af3ca9615da56c0366d47f.png">的基础解系,<img src="https://tihai-oss-cloud.itihey.com/img/721f4337e961a91c321a91dc475cf465.png">为任意常数,则<img src="https://tihai-oss-cloud.itihey.com/img/096ac92b2b262969bf4218c29a5bbbd5.png">的通解可表示为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/1b65a70d2d2b407ea2ce5caa063dac5b.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/06dd36f0e4aec109b350130a264d8ad9.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/7c70e93233137b6e0fe6f290e4993688.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/89e71666d78f7b6b262ab910cd3e4d3f.png">

若线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/096ac92b2b262969bf4218c29a5bbbd5.png">的系数矩阵<img src="https://tihai-oss-cloud.itihey.com/img/db70bceda2ae822f161e81ecd10fba66.png">是<img src="https://tihai-oss-cloud.itihey.com/img/b738d5f2052f64944ffb3ac2d61b0847.png">矩阵,且<img src="https://tihai-oss-cloud.itihey.com/img/9a0a5dba0fd206e24f0e5e74b8312389.png">,则( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/84e661836b9915933e74a89ce8e7503b.png">必有无穷多解B. <img src="https://tihai-oss-cloud.itihey.com/img/cd4246daccae3825b4f6dda81d1661a5.png">只有零解C. <img src="https://tihai-oss-cloud.itihey.com/img/84e661836b9915933e74a89ce8e7503b.png">一定无解D. <img src="https://tihai-oss-cloud.itihey.com/img/cd4246daccae3825b4f6dda81d1661a5.png">必有非零解

已知<img src="https://tihai-oss-cloud.itihey.com/img/da604db6b122d274b53d624361ff919f.png">是非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/78865f0a7d5a85930d5265966337d345.png">的两个不同的解,那么<img src="https://tihai-oss-cloud.itihey.com/img/16b50b0fe8412c8fa9947b807c0c834c.png">中,仍是线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/78865f0a7d5a85930d5265966337d345.png">特解的共有<img src="https://tihai-oss-cloud.itihey.com/img/84d8239b247391367cf1177f287922c3.png">

A. 2 个B. 1 个C. 3 个D. 4 个

方程组<img src="https://tihai-oss-cloud.itihey.com/img/2ba4894a09aa9a7d874e05c713e0512a.png">的通解为( ),其中<img src="https://tihai-oss-cloud.itihey.com/img/ba919b97d6283fcd7c530923c9dd3413.png">为任意常数

A. <img src="https://tihai-oss-cloud.itihey.com/img/0631d03f892229c6b8245cf9070086be.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/a41382dd3d4a33408161d6fbd8bc9726.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/d9392c360c39f30a023a918f051064b8.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/c2f5262241dc6122cb0022b389d88dc4.png">

设矩阵<img src="https://tihai-oss-cloud.itihey.com/img/60afb1f94d77cbab67aab3de69b71356.png">,<img src="https://tihai-oss-cloud.itihey.com/img/4332a4fadf18f2627ef495e1b635742c.png">,且方程组<img src="https://tihai-oss-cloud.itihey.com/img/84e661836b9915933e74a89ce8e7503b.png">无解,则<img src="https://tihai-oss-cloud.itihey.com/img/537acfcdd6926bd03b53d5f79908c200.png">=( )

A. 0B. 1C. 2D. 3

设四元非齐次线性方程组的系数矩阵的秩为3,已知<img src="https://tihai-oss-cloud.itihey.com/img/9bbdf57aede85e3a472677ff04e0ef97.png">是它的3个解向量,且<img src="https://tihai-oss-cloud.itihey.com/img/8e4e9ecb935e97c9a83a56b57e2c4ee3.png">那么该方程的通解为<img src="https://tihai-oss-cloud.itihey.com/img/84d8239b247391367cf1177f287922c3.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/07e3ced9ecb2a1ac01ffd3c44ffd0fd9.png">其中<img src="https://tihai-oss-cloud.itihey.com/img/d445b4123add1ba052cde20243b07dfe.png">为任意常数B. <img src="https://tihai-oss-cloud.itihey.com/img/0268ef5c2a54a81be9f0bd053e132ba9.png">其中<img src="https://tihai-oss-cloud.itihey.com/img/d445b4123add1ba052cde20243b07dfe.png">为任意常数C. <img src="https://tihai-oss-cloud.itihey.com/img/111a81d3b68107db62db1e5206ec58a4.png">其中<img src="https://tihai-oss-cloud.itihey.com/img/d445b4123add1ba052cde20243b07dfe.png">为任意常数D. <img src="https://tihai-oss-cloud.itihey.com/img/58dbc8b04028e8eade6cbd4684c9d348.png">其中<img src="https://tihai-oss-cloud.itihey.com/img/d445b4123add1ba052cde20243b07dfe.png">为任意常数

方程组<img src="https://tihai-oss-cloud.itihey.com/img/004878af783f8cae04ae855003647e3c.png">的解的情况为<img src="https://tihai-oss-cloud.itihey.com/img/e34a7e88d36492282243e5e2058df76e.png">

A. 有无穷多解B. 只有零解C. 无解D. 有唯一解

设<img src="https://tihai-oss-cloud.itihey.com/img/b25b5bfa350669a6c4ba89b88cd2028c.png">为 4 维列向量组, 且<img src="https://tihai-oss-cloud.itihey.com/img/5dfccdda04e3076fce1ce2b92dcff521.png">.已知线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/9574328db3f3edf3edfeab6e49877ce7.png">的通解为 <img src="https://tihai-oss-cloud.itihey.com/img/2afbfbc4af716625a717b9c93a2e5599.png">则向量组<img src="https://tihai-oss-cloud.itihey.com/img/b25b5bfa350669a6c4ba89b88cd2028c.png">的一个极大线性无关组为<img src="https://tihai-oss-cloud.itihey.com/img/84d8239b247391367cf1177f287922c3.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/539e78328e15b68d1cbb2da1aafca1b9.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/8835d4ab579c3b89882921662dc7073c.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/e78f5110113e7333361bc375e85077fc.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/6c9bce5214a911ff94e246c9459644fd.png">

线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/9ae497038692bf1793992d8a6b266c77.png">有唯一解的条件是<img src="https://tihai-oss-cloud.itihey.com/img/6a24482edc14b3b810df4e6b1b19acaa.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/109e1d5be48921e8cd9762c0c0a13730.png">B. 以上都不对C. <img src="https://tihai-oss-cloud.itihey.com/img/e6c5177ce757261e55c09f0e030a09f6.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/9c57ce0e1ca518a961ed3bf734ca0178.png">只有零解

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