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单选题设A,B均为n阶可逆矩阵,则下列运算关系正确的是( )

A.

B.

C.

D.

线性代数（2024春季）课程封面

学科：线性代数（2024春季）

时间：2024-06-27 16:32:51

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设A为m×n矩阵, C是n阶可逆矩阵, 矩阵A的秩为r1, 矩阵B = AC的秩为r, 则

A. r < r1B. r与r1的关系依C而定C. r > r1D. r = r1

设n阶矩阵A非奇异(n ³ 2), A*是A的伴随矩阵, 则

A. <img src="https://tihai-oss-cloud.itihey.com/img/29a37e539ca37ac1cb4783092efc6103.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/ef062d09bc1e16b40365c9c4dbb131ca.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/1f49ba607736e0854a116b10b97f4dac.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/1fe37ca48cb5e9dabf25b9d531f88e38.png">

若A是对称矩阵,则条件( )成立

A. <img src="https://tihai-oss-cloud.itihey.com/img/8c464ba5fb97aaa393bf9d1d14462676.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/61e42e80b66a1e07d5c0bd2b2cd121ac.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/74950bac5f22baeb2a4290700d025f30.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/cefc00fa26ec238ba33f00584785606e.png">

<img src="https://tihai-oss-cloud.itihey.com/img/934b9a17dfe817a877b8c42b69ac1b87.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/84d6f89ddd3e658011833e11c9abc9b1.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/4c252525d8eaf29fc6c30d7df6cc1a68.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/6e074053810330e64a2a2dcbcecd2983.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/2dd39f8a765e8a02dc45bff0f42a7d5d.png">

<img src="https://tihai-oss-cloud.itihey.com/img/75c7b1516e8e8856be58974c1a50a9b7.png">

A. 1B. 8C. 10D. 7

设A为3<img src="https://tihai-oss-cloud.itihey.com/img/779fbb7000a5a78a8c32af8afc718d18.webp">2矩阵,B为2<img src="https://tihai-oss-cloud.itihey.com/img/3cd617bf3ef0736a0f4e766831e60a69.webp">3矩阵,C为3<img src="https://tihai-oss-cloud.itihey.com/img/3cd617bf3ef0736a0f4e766831e60a69.webp">3矩阵,则下列运算有意义

A. AB-BCB. A+BC. BCD. AC

<img src="https://tihai-oss-cloud.itihey.com/img/c12fbeb49b31d7b0a80100ad61f6f282.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/d0ddcaa9059e48f4cef5ab9d08dbf7b8.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/6fcb7a6a0afea5632f879c1a071a2084.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/a6b89937ed233ce537c25fa6cb13f40c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/5d01c903e1c5537a13a6c379df61582c.png">

<img src="https://tihai-oss-cloud.itihey.com/img/4ca674d259c73e5ad4150ba24da7fd12.png">

A. 1B. 3C. 0D. 4

<img src="https://tihai-oss-cloud.itihey.com/img/e8db29b1cf8871370b6cf271c6de8f02.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/b3e0f6e535dd1a94e7260fdd1001cc52.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/ecadcc553a5b9e489c5608b8f2f09c06.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/a329c582c55082e2913f18fe7a0d44bf.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/d4c6eff41ba55da9d07c3c142ce7b615.png">

设A,B均为n阶可逆矩阵,则下列运算关系正确的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/ebab80da78f9b915186c74a09077ca02.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/285c3cbc5457998bb0bbf5fb0fa1534a.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/a833808507ba27b185bc8aab9e328571.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/c0be9b82722dd7353cd259ace2e14bb6.png">

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