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多选题 下列结论正确的是( )
D. 任意一个n阶矩阵A都可以表示为一个对称矩阵
和一个反对称矩阵
之和
学科：默认课程
时间：2026-05-22 16:39:39
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相关作业
题目1单选题
找出以下矩阵中的对角阵( )A. <img src="https://tihai-oss-cloud.itihey.com/img/69749f165ec94fce85b9fd62236aa75e.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d0add6c8af73dc21233819e39d7afd51.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/69f29f2c6061f96820ae33ce3fa4780b.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/00a32ae366291b2311e630b0287c1639.png">
题目2单选题
在矩阵<img src="https://tihai-oss-cloud.itihey.com/img/99f5dae0e840371b7f871046cbb30487.png">中,若当i<j时有<img src="https://tihai-oss-cloud.itihey.com/img/de5bda70f03134dcffddf490481b3194.png">,则称A为?矩阵( )A. 下三角B. 上三角C. 对角D. 无法确定
题目3单选题
以下命题中正确的是( )A. 元素全为1的矩阵称为单位矩阵B. 设对角矩阵<img src="https://tihai-oss-cloud.itihey.com/img/6605fa4f43f0d08e809c7aac504a2cce.png">,当<img src="https://tihai-oss-cloud.itihey.com/img/47ec2dd0af7b6e6028ade261fabacfd0.png">时,称<img src="https://tihai-oss-cloud.itihey.com/img/16f8b4532b2b1783c85ba709f08947a8.png">为数量矩阵C. 两个零矩阵相加,和仍为零矩阵D. 矩阵<img src="https://tihai-oss-cloud.itihey.com/img/f7d486c71333263a85d4ce987ec3e38b.png">是一个二阶反对称矩阵
题目4单选题
设矩阵<img src="https://tihai-oss-cloud.itihey.com/img/c5dbe3df73f238b016d31270fbcf6fc2.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/3fe29d468a73134eaf0c46a7e208cc0d.png">( )A. <img src="https://tihai-oss-cloud.itihey.com/img/9c13c71ac0222fd4d44baf971396071d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/76e183b71d64a09d934dd88955a78fb3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/62f7d97230567f86df6244380bba94d9.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/c2c40152c9038051cab9c33dd4b1697b.png">
题目5单选题
设矩阵<img src="https://tihai-oss-cloud.itihey.com/img/142ecfe60700643484c63f6dbe2c394a.png">,且<img src="https://tihai-oss-cloud.itihey.com/img/63bca2073cc37cc2107a7cd1fab456d2.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/31a512e43035a3d01a54b41424ea9a2d.png">( )A. <img src="https://tihai-oss-cloud.itihey.com/img/c6cff0e23ccf49b45f17da861ccf7bc0.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/8a8df918208a32f7cb01533c6ae93bf3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/02b3f21a542b4ac56bc1bb33affda241.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/10ae3ecf39bd4197620cabbb48a77985.png">
题目6单选题
若n阶矩阵的行列式为<img src="https://tihai-oss-cloud.itihey.com/img/047cc4f1e15a03355f5a066a74fee29e.png">( )A. 6B. <img src="https://tihai-oss-cloud.itihey.com/img/f5b3ebb226ac94baa0d3720a162b7bf3.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/f513e508278f56a816aa5d47f99f5277.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/71d907ecdf37ce5e288434cb5c26df7b.png">
题目7单选题
设A,B为同型矩阵,k,l为数,则以下结论中错误的是( )A. (kl)A=l(kA)B. k(A-B)=kA-kBC. 若kA=O,则A=OD. A-B=A+(-B)
题目8多选题
设A,B为n阶对称矩阵,则下列矩阵为对称矩阵的是( )A. A+BB. A-BC. ABD. lA
题目9多选题
下列结论正确的是( )A. 反对称矩阵一定是方阵,且主对角线元素全为0B. 对称矩阵的第i行元素与第i列元素对应相等,其中i=1,2,...,nC. 若A为奇数阶反对称矩阵,则有|A|=0D. 任意一个n阶矩阵A都可以表示为一个对称矩阵<img src="https://tihai-oss-cloud.itihey.com/img/c88a0f54aef581e50eb664bc15612f4e.png">和一个反对称矩阵<img src="https://tihai-oss-cloud.itihey.com/img/202a752571319ea686345545f822abe9.png">之和
题目10多选题
设A为n阶方阵,则下列关于方阵A的行列式说法正确的有( )A. <img src="https://tihai-oss-cloud.itihey.com/img/4d33e123c7aeaca2db4e0c6388287b99.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/a89bb10085267a5f58c6eceed33eabd8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/f1e3d43d0c82021b6a1040a7fd537348.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/6ffcd4da14e1d9e92522874692d0f228.png">
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