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单选题设3元非齐次线性方程组的两个解为,且系数矩阵的秩,则对于任意常数方程组的通解可表为( )

A.

B.

C.

D.

学科：默认课程

时间：2026-05-11 04:48:59

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已知<img src="https://tihai-oss-cloud.itihey.com/img/56a00dae372f82eda2636f19d49a5a40.png">是非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/dce5eb1515b87c671324d9b0a3b8446c.png">的两个不同的解,<img src="https://tihai-oss-cloud.itihey.com/img/e84435c40746f815d59396e608b63230.png">是导出组<img src="https://tihai-oss-cloud.itihey.com/img/4f8594e0aee0a400d8ba58679bda99c2.png">的基本解系,<img src="https://tihai-oss-cloud.itihey.com/img/0060d20e9364e113431ab4261fcc2e08.png">为任意常数,则<img src="https://tihai-oss-cloud.itihey.com/img/dce5eb1515b87c671324d9b0a3b8446c.png">的通解是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/1a7ae5bce8cc667e5580427ce428d6bb.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/4119167fce04be37e04a079782272105.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/2627536518d1fe8c151077d8b53e666d.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/b9425796b49a3885d7c3aefc3b9c0a00.png">

若<img src="https://tihai-oss-cloud.itihey.com/img/013aba1e37975d8b44e2da0bc731113f.png">是方程组<img src="https://tihai-oss-cloud.itihey.com/img/89be105c2879db8d7c571242b3744528.png">的解,<img src="https://tihai-oss-cloud.itihey.com/img/f1e401a3770e9c5cd6a95bdf3f5b3109.png">是方程组<img src="https://tihai-oss-cloud.itihey.com/img/66b2955bfaaa90d72363293fa139e07f.png">的解,则( )是方程组<img src="https://tihai-oss-cloud.itihey.com/img/69b897970aea45d84433041c106f9139.png">的解(<img src="https://tihai-oss-cloud.itihey.com/img/a7c6db7d8b323e5d50cb63b667701480.png">)

A. <img src="https://tihai-oss-cloud.itihey.com/img/48e74d6e294a1778c461c0473009314b.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/19aa553c22a42271119761f47db65161.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/7070ec9cb4fcda70ffedeb46bf2da5b1.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/cc66c36feb49ac17d231c0b5ae02d86c.png">

设含<img src="https://tihai-oss-cloud.itihey.com/img/0afaedf27cfaa44257eb0582d7a5f9a4.png">个方程<img src="https://tihai-oss-cloud.itihey.com/img/fcec676537dd39a35555be123ac2d18a.png">个未知变量的非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/82c82c9dce32d61dadadd6b5ba66349f.png">关于任意一个<img src="https://tihai-oss-cloud.itihey.com/img/0afaedf27cfaa44257eb0582d7a5f9a4.png">维常数向量<img src="https://tihai-oss-cloud.itihey.com/img/eb29bc9f078d582768533ab230ffeb06.png">都有解,则( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/1fcb6a104ca2a77828b282ef204174e4.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/f0d98d0362cb0dd8e7fa52a6bebbdee3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3ea1d3c91fbc2b6eacc15327d99268ad.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/71c4d7ca0518c1194bae607ff8c17dbe.png">

设向量<img src="https://tihai-oss-cloud.itihey.com/img/82f4935a7898748c3466ac45b83dcf2a.png">可以由向量组<img src="https://tihai-oss-cloud.itihey.com/img/d728acbffbb2f3f729fa1f7c141ddafc.png">线性表示,则数<img src="https://tihai-oss-cloud.itihey.com/img/0d604b5b9bc44cd334406594cc11ff91.png">应满足的条件是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/e486aeb4956d24e9965dc2ebb0da2a3a.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/2baae9d88c64c15f4c3d338bb3ccbc5c.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3b2f245c4147a6b88de7a85559ce2d43.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/be73a7765b3f23ad64e1ece0572fadd1.png">

设3元非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/6bf467ccc9e019492d02641d77290a4a.png">的两个解为<img src="https://tihai-oss-cloud.itihey.com/img/6ff13e08ebc2fa84c85d925383574fb9.png">,且系数矩阵<img src="https://tihai-oss-cloud.itihey.com/img/761bb4d7df77c707b6024812b4bf261a.png">的秩<img src="https://tihai-oss-cloud.itihey.com/img/aaf235396b8b0d040031a529f5ce707f.png">,则对于任意常数<img src="https://tihai-oss-cloud.itihey.com/img/30b627fc728555f53a5f2ad14aa6ca68.png"> 方程组的通解可表为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/3e0cd56b4ac74e48e568f022a7524490.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/9439d5c3e901924ed45d9b61397feb72.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/357701279b80a3da6c2d97ece920a544.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/867ea0af011d8a31d055c44c2b1049fc.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/e075e7ac2625869a713612797d691ce5.png">是<img src="https://tihai-oss-cloud.itihey.com/img/0397d32cfb356658455fcc1284424a41.png">的三个解向量,<img src="https://tihai-oss-cloud.itihey.com/img/a4d7f3857d74429dea962388a87ba8fe.png">,<img src="https://tihai-oss-cloud.itihey.com/img/cb2fc2d705b72ee703abe68496152097.png">, <img src="https://tihai-oss-cloud.itihey.com/img/23a81b84e22f391f2456df00a3eb2d3d.png">,<img src="https://tihai-oss-cloud.itihey.com/img/eb814780af2f12ac64c36a7d27db6cb4.png">为任意常数,则<img src="https://tihai-oss-cloud.itihey.com/img/0397d32cfb356658455fcc1284424a41.png">的通解为 ( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/409f9c080ed7245cfab2fbcb8b05505d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/ae236a4c3dad7b6513a62a4de5c49856.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/179472e47e3bc48162708d7319589750.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/7c0bece52b20ff77d692697709cdfc03.png">

当( )时,齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/e93bc3a0ce1ed07021c0605e4f86d4c5.png">一定有非零解

A. <img src="https://tihai-oss-cloud.itihey.com/img/aacd31be1425691e53ba871575956016.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/8c12c88fe957d4397d1258a61889dc25.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/391d3e27626a57af72e7fce2a319706b.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/f2686ba500406d78f1097b30340fc39b.png">

已知某个3元非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/6bf467ccc9e019492d02641d77290a4a.png">的增广矩阵<img src="https://tihai-oss-cloud.itihey.com/img/10b84a93f7e64e19d585ff083b51d9d9.png">经初等行变换化为:<img src="https://tihai-oss-cloud.itihey.com/img/836b649c740f024a13ac019560e6472b.png">,若方程组无解,则<img src="https://tihai-oss-cloud.itihey.com/img/6a4c7662318aee351b7b65c4c929daa8.png">____

设<img src="https://tihai-oss-cloud.itihey.com/img/e6692f5662e76386db8fb1c66aba7863.png">与<img src="https://tihai-oss-cloud.itihey.com/img/c4ebdc4db09c96d45962ac90c94243cc.png">均是方程组<img src="https://tihai-oss-cloud.itihey.com/img/6bf467ccc9e019492d02641d77290a4a.png">的解,则<img src="https://tihai-oss-cloud.itihey.com/img/e23b01b24a1f35b300d4d14ba19e5b2c.png">____

若<img src="https://tihai-oss-cloud.itihey.com/img/ef15ecce7cd2ca0b2aa3049bb11c1c24.png">都是<img src="https://tihai-oss-cloud.itihey.com/img/0397d32cfb356658455fcc1284424a41.png">的解,则<img src="https://tihai-oss-cloud.itihey.com/img/8f3f612df6fdc4f9c8dac36f0d26c921.png">是<img src="https://tihai-oss-cloud.itihey.com/img/bdd9ee952fc867a7a0e082ac03ae624f.png">的一个解

A. 正确B. 错误

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