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单选题 设m×n矩阵A的秩为r=m<n,
为m阶单位矩阵,下列结论中正确的是( )
C. 非齐次线性方程组
一定有无穷多个解
D. A经过初等行变换,必可以化为
的形式
学科：线性代数
时间：2023-06-26 06:44:58
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题目1单选题
已知mxn矩阵A的秩为r,若2≤r≤min(m,n)-1,则下列说法错误的是( )A. 矩阵A中所有的r阶子式都非零B. 矩阵A中所有的r+1阶子式都为零C. 矩阵A中存在一个非零的r-1阶子式D. 矩阵A中存在一个非零的r阶子式
题目2单选题
设m×n矩阵A的秩r(A)=n-3(n>3),<img src="https://tihai-oss-cloud.itihey.com/img/8044eb3cffb0e5a82bc050eb2f91decc.webp">是齐次线性方程组Ax=0的三个线性无关的解向量,则方程组Ax=0的基础解系为( )A. <img src="https://tihai-oss-cloud.itihey.com/img/db2a915361925e779090e7830e659f30.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/0d669f376b6e8a73510801056e51ffdd.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/98cfb0d20c7015875582ccc7bbe4eb01.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/c4e517e1f166aba6ffb900188b7ebdc5.webp">
题目3单选题
设向量<img src="https://tihai-oss-cloud.itihey.com/img/e02c9b4c74d4d59191c0dd71f98299d8.webp">可由向量组,<img src="https://tihai-oss-cloud.itihey.com/img/57b2c87174cc08b3d59d82e26a939710.webp">线性表示,但不能由向量组<img src="https://tihai-oss-cloud.itihey.com/img/4cb17f0108dac785fc012b05d1e05f6f.webp">线性表示,那么( )A. <img src="https://tihai-oss-cloud.itihey.com/img/b69588210488323e0791b47c05a5496a.webp">不能由<img src="https://tihai-oss-cloud.itihey.com/img/40746f303e528c365ceaa7582824453c.webp">线性表示,但可由<img src="https://tihai-oss-cloud.itihey.com/img/821c4851410af114b444ae308d70385c.webp">线性表示B. <img src="https://tihai-oss-cloud.itihey.com/img/b69588210488323e0791b47c05a5496a.webp">不能由<img src="https://tihai-oss-cloud.itihey.com/img/40746f303e528c365ceaa7582824453c.webp">线性表示,也不能由<img src="https://tihai-oss-cloud.itihey.com/img/821c4851410af114b444ae308d70385c.webp">线性表示C. <img src="https://tihai-oss-cloud.itihey.com/img/3cc407f1cc769be027af6ad6460f158f.webp">可由<img src="https://tihai-oss-cloud.itihey.com/img/40746f303e528c365ceaa7582824453c.webp">线性表示,但不可由<img src="https://tihai-oss-cloud.itihey.com/img/f22887bb6a18fbdcca4bdaf75e722a42.webp">线性表示D. <img src="https://tihai-oss-cloud.itihey.com/img/b69588210488323e0791b47c05a5496a.webp">可由<img src="https://tihai-oss-cloud.itihey.com/img/40746f303e528c365ceaa7582824453c.webp">线性表示,也可由<img src="https://tihai-oss-cloud.itihey.com/img/821c4851410af114b444ae308d70385c.webp">线性表示
题目4单选题
设A是n阶方阵,则|A|=0的充分必要条件为( )A. A的某两行对应元素成比例B. r(A)=nC. A的行向量组线性无关D. A的某个行向量可由其余行向量线性表示
题目5单选题
设向量组<img src="https://tihai-oss-cloud.itihey.com/img/b1c88a471e9365270e88b9a71d983e0d.webp">的秩为r(r<s),则( )A. <img src="https://tihai-oss-cloud.itihey.com/img/b1f73ba862e3e97c8c2b84305cfe6d23.webp">全是非零向量B. <img src="https://tihai-oss-cloud.itihey.com/img/b1f73ba862e3e97c8c2b84305cfe6d23.webp">线性无关C. <img src="https://tihai-oss-cloud.itihey.com/img/b1f73ba862e3e97c8c2b84305cfe6d23.webp">中任意r个向量都线性无关D. <img src="https://tihai-oss-cloud.itihey.com/img/b1f73ba862e3e97c8c2b84305cfe6d23.webp">中任意r+1个向量都线性相关
题目6单选题
a,b取何值时线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/88cca9374aab7323ca674df349d2e18e.webp">有唯一解( )A. a≠0且b≠0B. a=0或b=0C. a≠0或b≠0D. a=0且b=0
题目7单选题
设A为m×n矩阵,则齐次线性方程组Ax=0有非零解的充要条件是( )A. r(A)<nB. |A|=0C. m<nD. m>n
题目8单选题
设m×n矩阵A的秩为r=m<n,<img src="https://tihai-oss-cloud.itihey.com/img/460bafb754d85bbb7fb33b238926c1b1.webp">为m阶单位矩阵,下列结论中正确的是( )A. A的任意m个列向量必线性无关B. 齐次线性方程组AX=0只有零解C. 非齐次线性方程组<img src="https://tihai-oss-cloud.itihey.com/img/8b3b4b22925fe71410f8e253fa2dbeb6.webp">一定有无穷多个解D. A经过初等行变换,必可以化为<img src="https://tihai-oss-cloud.itihey.com/img/75cb375329f0cc39e11424bf7bb4ff12.webp">的形式
题目9单选题
已知<img src="https://tihai-oss-cloud.itihey.com/img/f97515b4c318370468331889b8908703.webp">是非齐次线性方程组Ax=b的两个不同解,<img src="https://tihai-oss-cloud.itihey.com/img/30931422410e9735a02e92d0f836ecd2.webp">是对应齐次线性方程组Ax=0的基础解系,<img src="https://tihai-oss-cloud.itihey.com/img/aa127c311e2602bde70fd94f2342ca78.webp">为任意常数,则方程组Ax=b的通解是( )A. <img src="https://tihai-oss-cloud.itihey.com/img/9ba93b8374c85e176376c9af14e5b552.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/875daffca06168b23247ccec35134704.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/ad5da274c956463859f36b71d656b9f0.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/92316d175ca118538e08fff2f35ea120.webp">
题目10单选题
设向量组<img src="https://tihai-oss-cloud.itihey.com/img/0c95fe0cc450a5a647a08d102c2a1414.webp">线性相关,则a=( )A. 3B. 1C. 5D. 7
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