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单选题设含个方程个未知变量的非齐次线性方程组关于任意一个维常数向量都有解,则( )

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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