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【百年教育职业培训中心】线性代数-章节资料考试资料-北京理工大学 (2)

来源：百年教育职业培训中心　更新时间：2022-05-30 16:30:09

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第一周单元测验

1、【单选题】<img src="http://nos.netease.com/edu-image/82746CACCA4EEC46BF931542DECCD41C-1444186154710?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img0.ph.126.net/S0KDtEclsFQ0ZajMkbnoaQ==/6630697230282603207.png" />

B、<img src="http://img1.ph.126.net/W1KN3esGxmXKSp_KFAvRqw==/6631268976327741580.png" />

C、<img src="http://img0.ph.126.net/d39Mo5XasXv8AV48cU6TRQ==/6631392121630052637.png" />

D、<img src="http://img1.ph.126.net/oRKzFRvaEjW94FIeXChgUw==/6630857758979808862.png" />为任意数

2、【单选题】<img src="http://nos.netease.com/edu-image/E73EB6C9308B1090BC8210DE51016E4D-1444304697430?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img2.ph.126.net/IbbkxpTBwbXG5dlbTdcWpQ==/6630233236375019702.png" /> ≠ 0

B、<img src="http://img1.ph.126.net/dsYLJc73QRlbLCKeW4hrbw==/6630623563003544869.png" />

C、<img src="http://img2.ph.126.net/BlxQaTfBc1N7q6zHYn4xiw==/6630170564212222454.png" />

D、<img src="http://img2.ph.126.net/kQT0rWsxBCEibByc55mlfA==/6631411912839353378.png" />

3、【单选题】下列矩阵中，（）是简化阶梯形矩阵.

A、 <img src="http://img1.ph.126.net/QlKFagaUidaCapJyvsJc-Q==/6630600473259346603.png" />

B、<img src="http://img1.ph.126.net/aAXcwa2If9rXzwlkcPj4ZA==/6631232692444029439.png" />

C、<img src="http://img1.ph.126.net/Hv2K8Zf950TV1TZpvGJt6A==/6619208433281768413.png" />

D、<img src="http://img1.ph.126.net/KPEElLjwpGO6rL95rvLegw==/6630063911584330120.png" />

4、【单选题】下列说法正确的是（）.

A、<img src="http://img2.ph.126.net/kFCsignoGQhBh9uACJMsMw==/6630128782770366857.png" />是一个方程组

B、若某个增广矩阵的一行是（0 0 0 3 0），则对应的线性方程组无解

C、若一个非齐次线性方程组的方程的个数多于未知数的个数，则这个方程组一定无解

D、若一个非齐次线性方程组中，方程的个数等于未知数的个数，则这个方程组一定有解且解唯一

5、【单选题】下列方程组中（）是线性方程组

A、<img src="http://img1.ph.126.net/rqFgjtSQpH69TH7HaKts5Q==/6619067695794250177.png" />

B、<img src="http://img0.ph.126.net/0_s3i_HpoOE2jyTOumEcqA==/3109454067740871396.png" />

C、<img src="http://img1.ph.126.net/Uv8N6LCmCfy2RpkofE4nRQ==/6630686235166352050.png" />

D、<img src="http://img1.ph.126.net/kW1rRaIlqVFCgoBdk7zYyg==/1322369440604794843.png" />

6、【单选题】<img src="http://nos.netease.com/edu-image/55AE026435617682382E8400327A8AC4-1444311995110?imageView

A、<img src="http://img1.ph.126.net/eO91S7boF3lzkJ2nDnBxrQ==/6630832470212823013.png" />

B、<img src="http://img2.ph.126.net/5rALNanqRkyQLZgzfcwU_A==/6631279971444018356.png" />

C、<img src="http://img0.ph.126.net/A1D3IyrMdDkFsD42id4Skw==/6630066110607586038.png" />

D、<img src="http://img0.ph.126.net/CnnC4Xk1vjk5Sqeu9g8zdQ==/6630552094747076199.png" />≠ 0

7、【单选题】下列增广矩阵中（）对应的方程组有唯一解（其中*表示任意常数）.

A、<img src="http://img2.ph.126.net/7elkpL9G922wJ2uZoLn-fg==/6630192554444776952.png" />

B、<img src="http://img0.ph.126.net/Vtz9eXVzON2bD5-R7_zf1Q==/6631426206490510440.png" />

C、<img src="http://img0.ph.126.net/S1GcCvf78ZqaEB6E3OKgrQ==/6631399818211445865.png" />

D、<img src="http://img0.ph.126.net/xaK4H0hc5Zp40yLCMy6jiw==/6630565288887273669.png" />

8、【单选题】<img src="http://nos.netease.com/edu-image/697D8C112E80516DEB89801B5E2098AA-1444186797711?imageView

A、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

B、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

C、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

D、<img src="http://img2.ph.126.net/hosf37-sNaNufMwCaYh_Fw==/6608259496492814132.png" />

9、【单选题】<img src="http://nos.netease.com/edu-image/71D22F3F8D5572C75E0846351814D9CF-1444351519680?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img1.ph.126.net/knoGV4UX9L4YUquOIP-Jxw==/1409626683467679913.png" />≠ 1且<img src="http://img1.ph.126.net/knoGV4UX9L4YUquOIP-Jxw==/1409626683467679913.png" />≠ <img src="http://img0.ph.126.net/IkxMY9N1n18bExa2LUs7ug==/6608646524584900572.png" />

B、<img src="http://img0.ph.126.net/inZusZjM_bG21RBZMME9LA==/6630938023328854908.png" />

C、<img src="http://img0.ph.126.net/BhgMrINeleV4pbKtjzXYaA==/6630465233328283158.png" />

D、<img src="http://img0.ph.126.net/inZusZjM_bG21RBZMME9LA==/6630938023328854908.png" />或<img src="http://img0.ph.126.net/BhgMrINeleV4pbKtjzXYaA==/6630465233328283158.png" />

10、【单选题】<img src="http://nos.netease.com/edu-image/A7BBB8F4FF38C688157BC830CCDA9C2A.png?imageView

A、有唯一解

B、有无穷多解

C、无解

D、无法判断

11、【单选题】<img src="http://nos.netease.com/edu-image/3E1970D85E50C97FF07F5A929CE33DE3.png?imageView&thumbnail=520x520&quality=100" />

A、一定有解

B、可能有解

C、一定无解

D、可能无解

12、【单选题】<img src="http://nos.netease.com/edu-image/06ACF68DE9B44D3C730EA0462B14B09A.png?imageView

A、<img src="http://img1.ph.126.net/fOkbsoF0DTzCj80myAyg9g==/6631436102099681746.png" />

B、<img src="http://img0.ph.126.net/ALJvReb9zf_D03h3HKU_4w==/6631369031890386213.png" />

C、<img src="http://img0.ph.126.net/NzDgjo65ZZnWFZy_ABhqrg==/6631330548978928104.png" />

D、<img src="http://img0.ph.126.net/AhQe1XUkmQKcZLzqypqDog==/6631229393913643479.png" />

13、【多选题】下列说法正确的是（）.

A、对增广矩阵作初等行变换不改变相应的线性方程组的解集合

B、存在只有两个解的线性方程组

C、两个同解的线性方程组中，方程的个数可能是不相同的

D、若两个矩阵的行数相等，则它们是行等价的

14、【多选题】下列说法正确的是（）.

A、矩阵的阶梯形的非零行数是唯一的

B、矩阵的简化阶梯形是唯一的

C、一个矩阵是零矩阵的充分必要条件是该矩阵的秩等于零

D、矩阵的阶梯形是唯一的

15、【多选题】下列矩阵为简化阶梯形的是（）.

A、<img src="http://img2.ph.126.net/fA-HctmDDFbaLps5TTB8FQ==/6630736812701213603.png" />

B、<img src="http://img2.ph.126.net/WC4UjK56AuvbWX1C5nDTFg==/6630533403049392521.png" />

C、<img src="http://img0.ph.126.net/LUxAGrrJWVNU46uyPyRhOQ==/6631222796839377501.png" />

D、<img src="http://img0.ph.126.net/Ixdtrg1RevFjTYXslHJI_w==/6631256881699835307.png" />

16、【判断题】线性方程组中未知数个数为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_43ab517d-5298-44ed-85c0-3f4665bb9a5e.png" />,方程个数为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_d73a86c2-5ad1-48cb-97d9-028b460a0990.png" />,系数矩阵的秩为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_4c944655-d74c-4cd8-bf55-77b155004478.png" />, 则当<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_8cb25df3-9220-4aab-b51b-5ab93cb50a30.png" />时，方程组有唯一解。

A、正确

B、错误

17、【判断题】线性方程组中未知数个数为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_c5682718-0ead-4d58-8e7c-a7331e163e92.png" />,方程个数为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_590425e1-b2c1-4011-aab0-bffac657721c.png" />,系数矩阵的秩为<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_ed51bffd-8a84-43a5-bbd6-7719238ec552.png" />, 则当<img src="http://edu-image.nosdn.127.net/_PhotoUploadUtils_1576527a-5c76-4131-888c-278b8819c1b3.png" />时，方程组有无穷多个解。

A、正确

B、错误

18、【判断题】<img src="http://nos.netease.com/edu-image/4B8EC70D978374FD32729D4D00445BB3.png?imageView

A、正确

B、错误

第二周单元测验

1、【单选题】<img src="http://nos.netease.com/edu-image/1233CE66C3FEF741252C84F8019BD4FE-1444552209061?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img0.ph.126.net/inZusZjM_bG21RBZMME9LA==/6630938023328854908.png" />或<img src="http://img0.ph.126.net/BhgMrINeleV4pbKtjzXYaA==/6630465233328283158.png" />

B、<img src="http://img0.ph.126.net/WfrPcpGv8PXSYjTO7GlWKw==/6619401947328168612.png" />

C、<img src="http://img1.ph.126.net/QiwUYNg-SkCVXjn5_IrmpQ==/6631429505025073828.png" />且<img src="http://img2.ph.126.net/XwlAAHV7mNuhCk15tvFBJg==/6631449296234713766.png" />

D、<img src="http://img1.ph.126.net/qsD8hhagQvkRX9cgUbAbbQ==/6619418440002582448.png" />

2、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵. 如果<img src="http://img1.ph.126.net/VSpk1AwkEANGRQ1ckqNjYQ==/6630600473259395551.png" />, 那么以<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为系数矩阵的齐次线性方程组有非零解的充分必要条件为（）.

A、<img src="http://img2.ph.126.net/OweRAW8i1UgSwZhyOKHPvQ==/6630119986677380936.png" />

B、<img src="http://img2.ph.126.net/04kqxz6eaXUV9bBO9crGmg==/6630476228444782856.png" />

C、<img src="http://img1.ph.126.net/WdgEplKuuW4APJNCUJIN1Q==/6630515810863384684.png" />

D、<img src="http://img0.ph.126.net/or15Ln5hMACjtnbQjM-Qrw==/6630761001957064836.png" />

3、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵，<img src="http://img1.ph.126.net/VSpk1AwkEANGRQ1ckqNjYQ==/6630600473259395551.png" />. 若以<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为系数矩阵的齐次线性方程组只有零解，则必有（）.

A、<img src="http://img1.ph.126.net/6_kf0-HpOT8EYUz3_T-nPQ==/6619426136584913827.png" />

B、<img src="http://img1.ph.126.net/WdgEplKuuW4APJNCUJIN1Q==/6630515810863384684.png" />

C、<img src="http://img2.ph.126.net/4BshgsJKqjbhCp2LvYZbUw==/6608941193702221979.png" />

D、<img src="http://img2.ph.126.net/OweRAW8i1UgSwZhyOKHPvQ==/6630119986677380936.png" />

4、【单选题】若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵，则以<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为系数矩阵的齐次线性方程组（）.

A、当<img src="http://img1.ph.126.net/fUCWr8N4y-fldgRBeYXkdA==/6630818176560219475.png" />时，必有非零解

B、当<img src="http://img1.ph.126.net/fUCWr8N4y-fldgRBeYXkdA==/6630818176560219475.png" />时，只有零解

C、当<img src="http://img1.ph.126.net/1uF8hx2SH0E5D4XTblZzmw==/6631400917723145473.png" />时，只有零解

D、当<img src="http://img1.ph.126.net/1uF8hx2SH0E5D4XTblZzmw==/6631400917723145473.png" />时，必有非零解

5、【单选题】若<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />是<img src="http://img1.ph.126.net/iO__4-wYELhu4HhkbvtGuw==/6630660946397626834.png" />矩阵，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有（）行.

A、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

B、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

C、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

D、<img src="http://img2.ph.126.net/hosf37-sNaNufMwCaYh_Fw==/6608259496492814132.png" />

6、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/VQj3rOC68sxoJ-cYprLopA==/6631365733349615530.png" />矩阵. 若乘积<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />是<img src="http://img0.ph.126.net/bnyEzKINaRB2g7hb-HPwwQ==/6631318454351065230.png" />矩阵，则<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />的行数，列数分别为（）.

A、<img src="http://img1.ph.126.net/wXbUmkxKOpp5kF15Zq-N_w==/6631395420163879009.png" />

B、<img src="http://img0.ph.126.net/NzDgjo65ZZnWFZy_ABhqrg==/6631330548978928104.png" />

C、<img src="http://img0.ph.126.net/NE2R0PNQZVpvcMZDuAP_7Q==/6630741210747773022.png" />

D、<img src="http://img1.ph.126.net/ox1m8uQboxNXR3RuvTfA6A==/6630624662515221604.png" />

7、【单选题】<img src="http://nos.netease.com/edu-image/F048CBA6378D8652BA8977A0B89FF0C9-1444886203806?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img0.ph.126.net/IkxMY9N1n18bExa2LUs7ug==/6608646524584900572.png" />

B、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

C、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

D、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

8、【单选题】若<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />都是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵，则（）.

A、<img src="http://img1.ph.126.net/2nR4ydBq3wu90fwdgb3OtQ==/6630703827352419784.png" />，其中<img src="http://img1.ph.126.net/9Mt-LvqvFeE1BXc1bu2Mwg==/6631916588675292898.png" />为非负整数

B、<img src="http://img1.ph.126.net/PnLk7piGySEm_N_BALkOLQ==/6630884147259374752.png" />

C、<img src="http://img2.ph.126.net/7x16QNjxrvB9wZHU0KVgxw==/6631317354839437754.png" />

D、<img src="http://img0.ph.126.net/IAwpmllh4GJiBlEb8Xg8fQ==/6631298663141766153.png" />，其中<img src="http://img1.ph.126.net/vQs7qNG27PRvjguKUs8RJQ==/1139410705825568242.png" />为非负整数

9、【单选题】下列命题中，不正确的是（）.

A、如果<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" /> 都是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，且<img src="http://img0.ph.126.net/Z0xxgMYSJrhfo-gVoXbh8A==/6630802783398920862.png" />，那么<img src="http://img1.ph.126.net/MjHtM1X03StUMZaRIgtmoA==/6631271175351070564.png" />

B、如果<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" /> 都是<img src="http://img2.ph.126.net/01U9iIdD7ujjQ9Y263xN7w==/6630574084980343964.png" />矩阵，那么<img src="http://img0.ph.126.net/GrR_VhyWMx6l_cSFbi-Pzw==/6630445442119206270.png" />

C、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，<img src="http://img2.ph.126.net/819ljKUveipB7sYvOvFlwQ==/6608769669887245088.png" />是单位矩阵，那么<img src="http://img2.ph.126.net/QOQSNsJ5vrV9HzD9KAFL_g==/6630861057515193929.png" />

D、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，<img src="http://img1.ph.126.net/HjwPHYBsZ_O24pFw2HMjXQ==/6631509769376112097.png" />为非负整数，那么<img src="http://img0.ph.126.net/AjQbhX1QIdiaAHhD_2v72g==/6631223896351077924.png" />

10、【单选题】<img src="http://nos.netease.com/edu-image/DC0FF007191E405F0C5983F57927973D-1444887015063?imageView

A、<img src="http://img0.ph.126.net/RE2n6i2pNiN21q35lQFTmQ==/6630844564840778592.png" />

B、<img src="http://img0.ph.126.net/CElmULaFIcpVJYjXALoQYw==/6630450939677346594.png" />

C、<img src="http://img1.ph.126.net/XsxfBdKMx8G3pzBjHauOPg==/6631445997699903916.png" />

D、<img src="http://img2.ph.126.net/3C1SEjbh1pE7gug4zlR85A==/6631388823095243012.png" />

11、【多选题】假设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />为矩阵。以下命题正确的是（）.

A、<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />的非零行的个数不大于<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的非零行的个数

B、<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />继承了<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行数，<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />的列数.

C、如果<img src="http://img2.ph.126.net/pZhPbVrVwldwtRk0Cc6ajQ==/6630423451886650940.png" />或<img src="http://img0.ph.126.net/gpRuuCdakhzYmiJiAYrw1Q==/6630600473259396453.png" />，那么<img src="http://img0.ph.126.net/Z0xxgMYSJrhfo-gVoXbh8A==/6630802783398920862.png" />

D、如果<img src="http://img0.ph.126.net/Z0xxgMYSJrhfo-gVoXbh8A==/6630802783398920862.png" />，那么<img src="http://img2.ph.126.net/pZhPbVrVwldwtRk0Cc6ajQ==/6630423451886650940.png" />或<img src="http://img0.ph.126.net/gpRuuCdakhzYmiJiAYrw1Q==/6630600473259396453.png" />.

12、【多选题】以下矩阵为初等矩阵的是（）.

A、<img src="http://img0.ph.126.net/d7N6xNrCsqqRAYhvB7eAcA==/6630151872513953247.png" />

B、<img src="http://img0.ph.126.net/_AMr6Vb1LBpiB96d6ZzlLQ==/6631353638723154873.png" />

C、<img src="http://img1.ph.126.net/nKDw6Oie0yNtzP1ykaWeJA==/6630237634421552497.png" />

D、<img src="http://img1.ph.126.net/2SJd02YKF_-KakOfYcbHXw==/6631398718699890952.png" />

13、【多选题】如果<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />为矩阵，<img src="http://img2.ph.126.net/gb-5yiJlO7MTtzp8_5MwmQ==/6608425522748584130.png" />为常数，那么以下命题正确的是（）

A、<img src="http://img1.ph.126.net/-9OI6VgprFfA5nurq45QFg==/6631352539211604163.png" />

B、<img src="http://img1.ph.126.net/NLZVBmmu20k_xVyr7SjmSA==/6630151872514613167.png" />

C、<img src="http://img1.ph.126.net/Wzc14-WqLM1h6dq1xM3gTQ==/6630168365189026006.png" />

D、<img src="http://img2.ph.126.net/QNWhql6ISgOb7IRro1hh-w==/6630651050794318610.png" />

14、【判断题】如果<img src="http://img0.ph.126.net/dYG6OzyjGLVpvDDDXG_3sA==/6619242518143107810.png" />, 那么<img src="http://img1.ph.126.net/1yOqAJ46zBDSBGiXKQkXwg==/3307893926404077487.png" />或者<img src="http://img2.ph.126.net/HsExbY0wx5xToJMeNrtzVA==/1997064959862293303.png" />.

A、正确

B、错误

15、【判断题】如果<img src="http://img1.ph.126.net/eiFBCkjTvqJvwV5J01MMNw==/6630845664351403603.png" />, 并且<img src="http://img1.ph.126.net/jhomMSHvIrJXpSF-SMSnYg==/4858258098126489043.png" />, 那么<img src="http://img2.ph.126.net/jjOCPt77ZTTcWpbyS7YGTA==/6598196766135335021.png" />

A、正确

B、错误

16、【判断题】已知<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />是矩阵, 则<img src="http://img1.ph.126.net/0S1PcVojU7-RRQ1vuXcEyw==/6598126397391158488.png" />

A、正确

B、错误

第三周单元测验

1、【单选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />是矩阵，则下列命题错误的是（）.

A、<img src="http://img1.ph.126.net/YIC-fIjAybPexbMUzoIbNg==/6630919331631513013.png" />

B、<img src="http://img1.ph.126.net/yjC0uA_ayeVLdNDPLYAgLg==/6630458636258777839.png" />

C、对任意非零数<img src="http://img2.ph.126.net/gb-5yiJlO7MTtzp8_5MwmQ==/6608425522748584130.png" />，有<img src="http://img2.ph.126.net/MizfJMIKFIByUuyiOGp5KQ==/6630677439073397552.png" />

D、<img src="http://img2.ph.126.net/fvMZwOlDFe7juyoIhyNcJQ==/6630122185700637008.png" />

2、【单选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />都是可逆矩阵，则下列式子错误的是（）.

A、<img src="http://img2.ph.126.net/pNqFEG2a9ztnIwgse8gGWQ==/6630555393282019931.png" />

B、<img src="http://img2.ph.126.net/SbQcbyZE1YdrY4Y08eehcw==/6630317898770420036.png" />

C、<img src="http://img1.ph.126.net/a8pERKOWT87KqhCg2uDhOA==/6630411357258779380.png" />

D、<img src="http://img1.ph.126.net/a8tgJ6_NKZFjPjGwNgArkQ==/6630414655793662729.png" />

3、【单选题】设<img src="http://img0.ph.126.net/BcCPS1JeIVv36N_ZXyl34g==/6619345872234822633.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵。若 <img src="http://img2.ph.126.net/O1IsE3YRT-go-RUH5tiPWw==/6630590577654805451.png" />，则（）.

A、<img src="http://img1.ph.126.net/A0ZmrY4g9aOg5QbCURLNFQ==/6630870953119892638.png" />

B、<img src="http://img0.ph.126.net/emXJ2uHrv-fMaxdljiUTmg==/6630306903654142326.png" />

C、<img src="http://img0.ph.126.net/wNeAa9w7I-7xOe4VP_pvsw==/6630478427468072481.png" />

D、<img src="http://img1.ph.126.net/Svj_eLkRz6uURXUuhb2LEQ==/6630841266305939860.png" />

4、【单选题】设<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />满足<img src="http://img0.ph.126.net/OlnEWHLGOp1W4U8ReN6Y-Q==/6630445442119239111.png" /> ，则（）.

A、 <img src="http://img2.ph.126.net/I9LZhiuRDiZGNS7Y_rV90w==/6631245886583731085.png" />一定可逆，且其逆为<img src="http://img0.ph.126.net/_RJuSCxbhmRi_02Lw5_r2w==/6630856659468738720.png" />

B、 <img src="http://img2.ph.126.net/I9LZhiuRDiZGNS7Y_rV90w==/6631245886583731085.png" />不一定可逆

C、<img src="http://img0.ph.126.net/zo-mkuemsgrcUDIWrzdLFQ==/6630260724165776085.png" />可逆

D、<img src="http://img0.ph.126.net/IZP2UYXP7Nw33jH65wEtdQ==/6631418509909307247.png" />

5、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵。如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />满足<img src="http://img2.ph.126.net/h_KAFNUZZq2e2I9ACZQtsA==/6631438301118605180.png" />，那么矩阵<img src="http://img1.ph.126.net/9PtYo49mSmX-19AmfAeqmQ==/6631210702211658274.png" />与<img src="http://img2.ph.126.net/c28QMYxd62dozS_Exb7g2A==/6630850062398972150.png" />（）.

A、最多有一个为可逆矩阵

B、同时为不可逆矩阵

C、至少有一个为零矩阵

D、同时为可逆矩阵

6、【单选题】<img src="http://nos.netease.com/edu-image/3E0CA0218FFD6F1E397EE6AC3A27B4D0-1445092424499?imageView

A、<img src="http://img0.ph.126.net/b6R5VHpXLpo-nww5S2f1bQ==/6630413556282036180.png" />

B、<img src="http://img1.ph.126.net/640Q1mAYTqI8D1GGZhMeXw==/6630470730886684405.png" />

C、<img src="http://img2.ph.126.net/1EjKDDPmClLozMe-cw6-rw==/6630417954328547318.png" />

D、<img src="http://img0.ph.126.net/KA8r7qNALtf8K6QwBmmVFQ==/2657968205096846550.png" />

7、【单选题】<img src="http://nos.netease.com/edu-image/13E2367CD798398EBB4A66AB90554D3C.png?imageView

A、<img src="http://img0.ph.126.net/95zywXcG5qgIU79vPmFAVg==/6619323882003532494.png" />

B、<img src="http://img1.ph.126.net/N0f0y-L0jlXjeWP7TNx5rA==/6630126583747187155.png" />

C、<img src="http://img2.ph.126.net/e91MYOtA_hX2TTobO_f8OA==/6630430048956451565.png" />

D、<img src="http://img0.ph.126.net/isE0dUieV1x_T70ehWC-4w==/6619061098724492256.png" />

8、【单选题】设<img src="http://img0.ph.126.net/BcCPS1JeIVv36N_ZXyl34g==/6619345872234822633.png" />是矩阵，则下列命题正确的是（）

A、若<img src="http://img1.ph.126.net/UV8n1uYY8RooyJregD9DLQ==/6630920431143142423.png" />，且<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />可逆，则<img src="http://img2.ph.126.net/xuDHw22taWMUB5Z_T8qZBg==/6630559791328532345.png" />

B、若<img src="http://img2.ph.126.net/PEfW6uzzYHp77PKvdrTWyQ==/6630920431143142460.png" />，则<img src="http://img2.ph.126.net/pZhPbVrVwldwtRk0Cc6ajQ==/6630423451886650940.png" />或<img src="http://img0.ph.126.net/IZP2UYXP7Nw33jH65wEtdQ==/6631418509909307247.png" />

C、若<img src="http://img0.ph.126.net/iw9dw6T6JCEd8lnMrA2eow==/2813905342194499200.png" />，且<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />≠0，则<img src="http://img2.ph.126.net/xuDHw22taWMUB5Z_T8qZBg==/6630559791328532345.png" />

D、若<img src="http://img2.ph.126.net/WcVErNjZD6bfX6GWjWVRHQ==/6630488323072723691.png" />，则<img src="http://img2.ph.126.net/pZhPbVrVwldwtRk0Cc6ajQ==/6630423451886650940.png" />

9、【单选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，则下列矩阵为对称矩阵的是（）.

A、<img src="http://img2.ph.126.net/vkrbShaBt3XH-THkoERyng==/2878081636884561392.png" />

B、<img src="http://img2.ph.126.net/2tXOi-sgDfuC01g-TObeSQ==/1355864962833357491.png" />

C、<img src="http://img1.ph.126.net/E-ZYnJ8TuieH5NUoxeRHTw==/6630627961050155215.png" />

D、<img src="http://img2.ph.126.net/W1PszyqraNht2SM6XJUQ5g==/6630078205235565842.png" />

10、【单选题】以下说法不正确的是（）.

A、<img src="http://img2.ph.126.net/ldDqYL98nHuJoKLj0efpiQ==/6608506886608212686.png" />是<img src="http://img2.ph.126.net/uj5tY4B4dkdalhHF2sxkMg==/2879207536790944073.png" />的子空间

B、<img src="http://img2.ph.126.net/s-ZEQx4rhsfn4D9Na7K4KA==/6630289311468098663.png" />为任意实数<img src="http://img2.ph.126.net/l12iRFR3uQ7XKxTSDY2vbg==/6630640055676431735.png" />是<img src="http://img2.ph.126.net/uj5tY4B4dkdalhHF2sxkMg==/2879207536790944073.png" /> 的子空间

C、一个子空间仍然是一个向量空间

D、零空间是向量空间

11、【多选题】下列命题正确的是（）.

A、任何一个方阵都可以表示成一个对称矩阵与一个反对称矩阵之和

B、对任意矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />，<img src="http://img2.ph.126.net/vkrbShaBt3XH-THkoERyng==/2878081636884561392.png" />和<img src="http://img2.ph.126.net/byWjAfCXyFDBg75ZNLnM-Q==/6630855559957112708.png" />都是对称矩阵

C、可逆上三角矩阵的逆仍然是上三角矩阵

D、下三角矩阵的转置仍然是下三角矩阵

12、【多选题】设<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />是可交换的，即<img src="http://img0.ph.126.net/AuCCZj8wlrqHGFyEZX2W3w==/6631264578281055564.png" />，则有（）.

A、当<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />都是对称矩阵时，<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />是对称矩阵

B、<img src="http://img2.ph.126.net/7x16QNjxrvB9wZHU0KVgxw==/6631317354839437754.png" />

C、<img src="http://img2.ph.126.net/oZJzOnSST0kZ_LhVz9OtJQ==/6630173862747179366.png" />

D、当<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />都是反对称矩阵时，<img src="http://img2.ph.126.net/5BqbdYDaVjiUhhdzIk2W6g==/2173831245236992859.png" />是反对称矩阵

13、【多选题】以下命题正确的是（）.

A、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />等价的充分必要条件是存在初等矩阵<img src="http://img2.ph.126.net/pJPMI8CmbvgLgR8lsABPHw==/6631429505025599192.png" />和<img src="http://img2.ph.126.net/s4nYEmzvEErkEgmcE3znYA==/6631408614304674260.png" />，使得<img src="http://img1.ph.126.net/ezSXQuUuk22gGH4Hmlo0ZQ==/6630504815747142094.png" />

B、每个初等矩阵都是可逆的

C、若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />可经过初等行变换化为单位矩阵，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />可逆‍

D、若干个<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶可逆矩阵的乘积是可逆的，且其逆为这些矩阵的逆按照相同顺序的乘积

14、【多选题】如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />实矩阵，那么（）.

A、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的零空间<img src="http://img0.ph.126.net/d9AEm8seMQihPxGUC2V5gw==/6630868754096638302.png" />是向量空间<img src="http://img1.ph.126.net/JqhgDbSYs1_EhHfOEea4TQ==/6630619164955704790.png" />的子空间

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的列空间<img src="http://img1.ph.126.net/OtyocC2RR8T8C-FjMv1v1A==/6630841266305941342.png" />是向量空间<img src="http://img0.ph.126.net/lauSjqpU1ll7uBfQSKTGmw==/2528208240833224665.png" />的子空间

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的列空间<img src="http://img1.ph.126.net/OtyocC2RR8T8C-FjMv1v1A==/6630841266305941342.png" />是向量空间<img src="http://img1.ph.126.net/JqhgDbSYs1_EhHfOEea4TQ==/6630619164955704790.png" />的子空间

D、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的零空间<img src="http://img0.ph.126.net/d9AEm8seMQihPxGUC2V5gw==/6630868754096638302.png" />是向量空间<img src="http://img0.ph.126.net/lauSjqpU1ll7uBfQSKTGmw==/2528208240833224665.png" />的子空间

15、【多选题】下列集合中，构成<img src="http://img1.ph.126.net/THPCCNiAhWm6hE-Rb52Ovw==/3672404021244231727.png" />上的向量空间的是( ).

A、<img src="http://img0.ph.126.net/jkQ84QqotmnJ6KZmEARzkQ==/2764084271316752856.png" />

B、<img src="http://img2.ph.126.net/KhB_0JaVWQJ4-zhKn8W9VQ==/6619405245863988281.png" />

C、<img src="http://img1.ph.126.net/7m-NQ_ORJjJ7CvBOzmzliw==/6630522407933181631.png" />

D、<img src="http://img2.ph.126.net/gwTUkessnEoIJSZWEJR-hg==/6630711523933689434.png" />

16、【判断题】如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" /> 与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />都是不可逆矩阵, 那么<img src="http://img2.ph.126.net/ca4977thk1mcJyw0AG9sjw==/6608182530679584932.png" />也是不可逆矩阵;

A、正确

B、错误

17、【判断题】<img src="http://nos.netease.com/edu-image/FB03A5093B507930A69E6E36C99849A8.png?imageView&thumbnail=520x520&quality=100" />

A、正确

B、错误

第四周单元测验

1、【单选题】下列各向量组线性相关的是（）.

A、<img src="http://img2.ph.126.net/-e8MfWMhT5un5I6gbIIMgQ==/6631364633839684562.png" />

B、<img src="http://img1.ph.126.net/m0sTRLBCe8Y6X8QQxqRLOQ==/6630575184492050761.png" />

C、<img src="http://img0.ph.126.net/t8yzE7tkw3novFCiHNTkog==/6619099581631469325.png" />

D、<img src="http://img1.ph.126.net/Pg8LRYSeA-BuGBAl--YW8Q==/6631281070955970196.png" />

2、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵. 如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的秩 <img src="http://img0.ph.126.net/WcAhvd_JekDXwIsqHdS-vw==/6631439400630372039.png" />, 那么在<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个行向量中（）.

A、必有<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个行向量线性无关

B、任意<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个行向量线性无关

C、任意<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个行向量都构成极大无关向量组　

D、任意一个行向量都可以由其余<img src="http://img2.ph.126.net/V8Q32Iqg5pjlD6xmArszqQ==/6631337146048988948.png" />个行向量线性表出

3、【单选题】设<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />元向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性无关, <img src="http://img0.ph.126.net/QgVN7P8SbLVrmzAB6BQFWA==/6608409030074225763.png" />为一<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />元向量, 则（）.

A、当<img src="http://img2.ph.126.net/Z10vGvyIzwqrRcvMXWeCew==/6630201350537900030.png" />时,<img src="http://img0.ph.126.net/QgVN7P8SbLVrmzAB6BQFWA==/6608409030074225763.png" />一定能被<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性表示

B、<img src="http://img0.ph.126.net/QgVN7P8SbLVrmzAB6BQFWA==/6608409030074225763.png" />一定能被<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性表示

C、 <img src="http://img0.ph.126.net/QgVN7P8SbLVrmzAB6BQFWA==/6608409030074225763.png" />一定不能被<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性表出　

D、<img src="http://img0.ph.126.net/On2LAR_DOGDuMc9XgyucEw==/6630178260793714911.png" />线性相关

4、【单选题】<img src="http://nos.netease.com/edu-image/4135BBE0633FEB9898514186C49B4270.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img1.ph.126.net/YksL--bfDIm0v9iKU1k7Zg==/6619585565770945237.png" />

B、<img src="http://img0.ph.126.net/wKN40nbh1CbOZ-AuqYo7Ww==/6630646652747859138.png" />

C、<img src="http://img1.ph.126.net/mzUrzPc9iPTyeF3UJTIGcg==/6619079790422169124.png" />

D、<img src="http://img2.ph.126.net/JIrFH0rJfoGUVA67Cmp1qA==/6631343743118767295.png" />

5、【单选题】向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />的秩不为零的充分必要条件是（）.

A、<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />中至少有一个非零向量

B、<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />全为非零向量

C、<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />的任一部分组均线性相关

D、<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性无关

6、【单选题】<img src="http://nos.netease.com/edu-image/1AEB354B94B88A7910041FE7CD479A71.png?imageView

A、<img src="http://img2.ph.126.net/3ueIpTCCoNhqfEtYNwy12Q==/6619237020584941694.png" />

B、<img src="http://img0.ph.126.net/Q1-DVkHx4fuisdigAP-8RQ==/6630719220515114871.png" />

C、<img src="http://img1.ph.126.net/jnbijysEVEW_w242NMMhvw==/6630546597189024055.png" />

D、<img src="http://img2.ph.126.net/0fDivtuJlpbpHLTIvWu0GA==/6630770897561792819.png" />

7、【单选题】<img src="http://nos.netease.com/edu-image/3855C10A27E62208A4F89CD0DF60654D.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img0.ph.126.net/3ZtNt8cHZzkC6hPEK5XnAQ==/6630583980585074376.png" />

B、<img src="http://img0.ph.126.net/nzRnDx0uqf8M6C3JdW4dsg==/6630700528817622621.png" />

C、<img src="http://img2.ph.126.net/_A6EoAVv2m2crvh3jD6F9A==/6631315155816436811.png" />

D、<img src="http://img1.ph.126.net/B152dS1lyOze1KgQm1PE8Q==/6631207403676913333.png" />

8、【单选题】<img src="http://nos.netease.com/edu-image/8A3A73CDB64FC6B70D385C085D38E4DC.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img0.ph.126.net/bDeNV_BiXf2RUl9IpRwsDQ==/6631223896351330881.png" />

B、<img src="http://img2.ph.126.net/KXO0SfyZ2cjozEX26S4hbg==/2406048100939730810.png" />

C、<img src="http://img0.ph.126.net/J7rx3O4DgFpz3WIuUpirbg==/6630851161910634651.png" />

D、<img src="http://img2.ph.126.net/wVvPJYPhz-oPL5LcgD8ZIw==/6631329449467595573.png" />

9、【单选题】若向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />的秩为<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />，则（）.

A、向量组中任意<img src="http://img0.ph.126.net/t0eT3IAprWVislltjvxkiw==/6619453624375611384.png" />个向量必定线性相关

B、向量组中任意小于<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个向量的部分组线性无关

C、向量组中任意r个向量线性无关

D、必定<img src="http://img0.ph.126.net/afBz-j-4_UEYaVc9xoDI0g==/6630291510491378643.png" />

10、【单选题】若向量组<img src="http://img2.ph.126.net/KXO0SfyZ2cjozEX26S4hbg==/2406048100939730810.png" />线性无关，则下列向量组线性相关的是（）.

A、<img src="http://img2.ph.126.net/tG0v2kNRza9FM_hR3UQKzg==/6631261279746672767.png" />

B、<img src="http://img0.ph.126.net/3p97HKzQekIq7kIlVRa3Jw==/975592269296195193.png" />

C、<img src="http://img1.ph.126.net/Q1USkQqZygVmciIMM6zrBg==/6619439330724450394.png" />

D、<img src="http://img2.ph.126.net/EALDBj_x8haG-JI2Kw8kWw==/6631293165583886126.png" />

11、【单选题】<img src="http://nos.netease.com/edu-image/AFDD582FAEC5B42E09C0012D0F151C6B.png?imageView

A、<img src="http://img0.ph.126.net/WUEfXMfsJOAunqzH3MhuZg==/3670152221430749034.png" />

B、<img src="http://img2.ph.126.net/jkpaPy_zAokYqW8qJeFisQ==/6619384355142185462.png" />

C、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

D、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

12、【单选题】<img src="http://nos.netease.com/edu-image/AAF5560F69467E2A172C974FE096EC0E.png?imageView

A、<img src="http://img2.ph.126.net/KXO0SfyZ2cjozEX26S4hbg==/2406048100939730810.png" />

B、<img src="http://img0.ph.126.net/J7rx3O4DgFpz3WIuUpirbg==/6630851161910634651.png" />

C、<img src="http://img1.ph.126.net/0QQ7GYXJuBTkHderX5R8KA==/6630908336515270036.png" />

D、<img src="http://img0.ph.126.net/0cC7YC8fTIAa2KvLXx90Bg==/1171217378110704765.png" />

13、【单选题】<img src="http://nos.netease.com/edu-image/4CF6311884DC64B27CFF2EE3C8F62B36.png?imageView

A、<img src="http://img0.ph.126.net/Wv31FtPpcyg_YXoMfUyaFw==/6631292066072258475.png" />

B、<img src="http://img0.ph.126.net/tN8nWY8Zv92lsy7Q4gOGeg==/6631352539211789964.png" />

C、<img src="http://img1.ph.126.net/7XK-0jqW1d38SPOSCc4NAA==/6631445997700162777.png" />

D、<img src="http://img0.ph.126.net/cJhysShNtwJaKA417nQ34g==/6631326150932712786.png" />

14、【多选题】设向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />的秩为<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />，则下列说法错误的是（）.

A、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中任意<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个向量线性无关

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中任意<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />个向量线性相关

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中任意<img src="http://img0.ph.126.net/t0eT3IAprWVislltjvxkiw==/6619453624375611384.png" />个向量线性无关

D、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中任意<img src="http://img0.ph.126.net/t0eT3IAprWVislltjvxkiw==/6619453624375611384.png" />个向量线性相关

15、【多选题】下列命题中，错误的是（）.

A、若向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性相关，则<img src="http://img2.ph.126.net/WnDhO_xGF9v16vYuUEEa_g==/6619146860630613239.png" />一定可由<img src="http://img2.ph.126.net/29uSgLV05NLX1O416zSUdw==/6630423451886711294.png" />线性表示

B、若存在一组实数<img src="http://img1.ph.126.net/dxZgeyzpbOtCYnEQQatl7Q==/6630718121003487664.png" />,使得<img src="http://img0.ph.126.net/ZvfnvDx4NYqtZp6snmn1qw==/6630862157026904739.png" />，则称向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性相关

C、若向量组<img src="http://img2.ph.126.net/xKsGwJobzS4JcJzH1PWB7w==/6631211801723426078.png" />线性相关，则向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />必线性相关

D、向量组<img src="http://img0.ph.126.net/ByH_ES4vTGiuiVo3eBvAfg==/2826290241169483377.png" />线性相关的充要条件是它所构成的矩阵的秩<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />小于向量个数<img src="http://img0.ph.126.net/LsthuCjzv-tCT_rsXhlRxw==/3678877945708590189.png" />

16、【判断题】线性相关的向量组至少有一个部分组(真子集)也是线性相关的

A、正确

B、错误

17、【判断题】<img src="http://nos.netease.com/edu-image/09D2602E21B0C26F2F483C7A6BB4FA6B.png?imageView&thumbnail=520x520&quality=100" />

A、正确

B、错误

18、【判断题】<img src="http://nos.netease.com/edu-image/53A57814A57DDDC7E906F7941B22E731.png?imageView&thumbnail=520x520&quality=100" />

A、正确

B、错误

19、【判断题】<img src="http://nos.netease.com/edu-image/683837CB6F743765A6FEEA7BBAE756AF.png?imageView&thumbnail=520x520&quality=100" />

A、正确

B、错误

第五周单元测验

1、【单选题】齐次线性方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />只有零解的充分必要条件是（）.

A、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的列向量组线性无关

B、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的列向量组线性相关

C、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行向量组线性无关

D、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行向量组线性相关

2、【单选题】齐次线性方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />有非零解的充分必要条件是（）.

A、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中必有一列向量可以由其余列向量线性表示

B、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的任意两个列向量线性无关

C、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的任意两个列向量线性相关

D、矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的任一列向量都可以由其余列向量线性表示

3、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵. 如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的秩为<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />, 那么齐次线性方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />的基础解系中向量个数为（）.

A、<img src="http://img2.ph.126.net/lhddkYuIAAubJzC4nX4CJg==/6608604743143843901.png" />

B、<img src="http://img2.ph.126.net/UFnDQFOp101XeTFk01C50A==/3680848270545578279.png" />

C、<img src="http://img0.ph.126.net/gfyUsw8yWnr5CqDjIzP1Og==/6631200806607342189.png" />

D、<img src="http://img1.ph.126.net/Q-jRslpIR4KSA2FBR_6yew==/6630490522095247156.png" />

4、【单选题】设<img src="http://img1.ph.126.net/AsG-Op2T1ssWUSLnylSWag==/6608641027027070572.png" />是齐次线性方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" /> 的一个基础解系，下列哪一组向量也是基础解系（）.

A、<img src="http://img1.ph.126.net/59DEyFJYaOHBnGzy0EleaQ==/6630103494003047260.png" />

B、<img src="http://img1.ph.126.net/FbqLwkQQILEvmSJL_mAZ-w==/6630758802933922894.png" />

C、<img src="http://img1.ph.126.net/kKC-AyS1mmKCQfDV5J-j2g==/6630877550189719222.png" />

D、<img src="http://img2.ph.126.net/cocSbBgo9WeNJkYMf9AjvQ==/6630658747375794191.png" />

5、【单选题】设<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的秩为<img src="http://img1.ph.126.net/LowUWiWPkEdRRSOV__sXwg==/6630695031259513477.png" />，<img src="http://img1.ph.126.net/A8Vv3LY002-TAc397PuoHA==/1181069002296130786.png" />为<img src="http://img1.ph.126.net/vQs7qNG27PRvjguKUs8RJQ==/1139410705825568242.png" />阶单位矩阵，下列结论中正确的是（）.

A、非齐次线性方程组<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />一定有无穷多个解

B、齐次线性方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />只有零解

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />经过初等行变换，必可以化为<img src="http://img0.ph.126.net/DP8ND1YaoZm2nQkT_B6UvA==/6630327794375113770.png" />的形式

D、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的任意<img src="http://img1.ph.126.net/vQs7qNG27PRvjguKUs8RJQ==/1139410705825568242.png" />个列向量必线性无关

6、【单选题】设<img src="http://img1.ph.126.net/1fnd7t3AYVRGaLUXzHpKyA==/2780409819965978167.png" />是非齐次线性方程组<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />的两个解, 则下列向量中仍为方程组解的是（）.

A、<img src="http://img2.ph.126.net/2hpolRvBKf-B2KebcPmDiA==/2407174000847896643.png" />

B、<img src="http://img1.ph.126.net/fMO5jAyrLQmeljj6NpqIuw==/632474272686837718.png" />

C、<img src="http://img0.ph.126.net/4sDUvSHsSuNYXeGq9KVLNQ==/6630921530654831592.png" />

D、<img src="http://img2.ph.126.net/VmkEDv-7DPAFNS9fFaR2cg==/6630472929908776211.png" />

7、【单选题】<img src="http://nos.netease.com/edu-image/CE8386B5ECDA2F246324FF8F2B0F11C3.png?imageView

A、<img src="http://img0.ph.126.net/Jf0hCBKz4Zr4Q6OLiI0cEw==/6630439944561147648.png" />

B、<img src="http://img2.ph.126.net/vWhDnrwletwdaGmkCIGgIw==/2890748010836580347.png" />

C、<img src="http://img1.ph.126.net/GzZPlKFQYljbhDkdatWNgg==/6631237090491062200.png" />

D、<img src="http://img0.ph.126.net/69YT19088k4gixZm5M5-pw==/6631442699165476422.png" />

8、【单选题】已知<img src="http://img0.ph.126.net/aHx4iT13zXd-jaWHy-4x9g==/6631256881700356842.png" />是非齐次线性方程组<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />的两个不同的解，<img src="http://img1.ph.126.net/1fnd7t3AYVRGaLUXzHpKyA==/2780409819965978167.png" />是其导出方程组<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />的基础解系，<img src="http://img2.ph.126.net/Gc5OHJOF8zeRiJ7FtaH8pQ==/6631312956793377137.png" />为任意常数，则方程组<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />的通解是（）.

A、<img src="http://img1.ph.126.net/A2ruke-JxEeETNlxNKSBPQ==/6630467432351847961.png" />

B、<img src="http://img1.ph.126.net/qsK69tW7yer49IdlXsU7cA==/6630787390236240493.png" />

C、<img src="http://img0.ph.126.net/6y83gXI-QkbKikacCG9l8w==/6630078205235612820.png" />

D、<img src="http://img1.ph.126.net/qEJObMVmdvEiFQq3Vp-p5g==/6631231592932921165.png" />

9、【单选题】对任意的<img src="http://img0.ph.126.net/KGr_c2Q_VBpK57CrJgMkoA==/6630325595350014414.png" />,关于内积运算下列各式中错误的是（）.

A、<img src="http://img2.ph.126.net/z335vXIwZxnOlZ6n5RjUNQ==/6630334391444880605.png" />

B、<img src="http://img2.ph.126.net/IHkJSDnGGVwb58qHWKzOqw==/6631299762653847071.png" />

C、<img src="http://img1.ph.126.net/uqWZCiDjdKTABxjTMs6QtQ==/6630933625282747759.png" />

D、<img src="http://img0.ph.126.net/NJRXwCZE0Q_B3R9XHu_3gA==/1056938537566883421.png" />并且<img src="http://img2.ph.126.net/cu-gen51qQxOSMf6xmgXXw==/6631430604537548627.png" />当且仅当<img src="http://img1.ph.126.net/vzNTR1aWNjsAom3y7cFfeA==/6630854460443174032.png" />

10、【单选题】关于正交向量组，以下命题正确的是（）.

A、正交向量组一定是线性无关的向量组

B、线性无关的向量组一定是正交向量组

C、正交向量组可以包含零向量

D、只含一个向量的向量组不可能是正交向量组

11、【单选题】<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶实方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个列向量构成一组规范正交基，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是（）.

A、正交矩阵　

B、对称矩阵

C、反对称矩阵

D、对角矩阵

12、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是2阶矩阵，下列命题错误的是（）.

A、如果互换<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的两列得到<img src="http://img1.ph.126.net/aqNrnUku8uNiaB3eqnbc7Q==/6630430048956497875.png" /> 则<img src="http://img2.ph.126.net/UtMwngKPrYxI0-DizL2ufw==/6630613667399059469.png" />

B、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的两列对应元素成比例，则<img src="http://img1.ph.126.net/Ozdp5L9Mbzd_9FBGamwdOg==/6630430048956497887.png" />

C、如果<img src="http://img2.ph.126.net/gb-5yiJlO7MTtzp8_5MwmQ==/6608425522748584130.png" />是常数，则<img src="http://img2.ph.126.net/LElruYKyZ7gpcKmYifFAjg==/1009369266502620629.png" />

D、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的某列的<img src="http://img2.ph.126.net/gb-5yiJlO7MTtzp8_5MwmQ==/6608425522748584130.png" />倍加到另一列得到矩阵<img src="http://img1.ph.126.net/aqNrnUku8uNiaB3eqnbc7Q==/6630430048956497875.png" /> 则<img src="http://img2.ph.126.net/WNpNpAV7EKXE8-m159MKoQ==/6630308003165817239.png" />

13、【单选题】设<img src="http://img1.ph.126.net/6ehCuvHw_aW4la2lalfnqg==/6619505301421164532.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />中元素<img src="http://img2.ph.126.net/oURrF5n4pWc711j8LJLZKA==/4915960468351830467.png" />的代数余子式，则下列命题中错误的是（）.

A、<img src="http://img2.ph.126.net/oURrF5n4pWc711j8LJLZKA==/4915960468351830467.png" />的余子式和代数余子式互为相反数

B、<img src="http://img2.ph.126.net/F-E-nBRDJSYbzPwUCeaPug==/6631657103934511127.png" />

C、<img src="http://img0.ph.126.net/ASJSSonlT8vLdJh3tblMnw==/3831437383085640003.png" />的展开式有<img src="http://img2.ph.126.net/_NZHsmVRzivmkHcCD7kteg==/6619136965025502395.png" />项

D、若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为对角矩阵，则<img src="http://img0.ph.126.net/ASJSSonlT8vLdJh3tblMnw==/3831437383085640003.png" />等于矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />主对角线上元素的乘积

14、【多选题】设<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />是一非齐次线性方程组, <img src="http://img0.ph.126.net/aHx4iT13zXd-jaWHy-4x9g==/6631256881700356842.png" />是其任意2个解, 则下列结论正确的是（）.

A、<img src="http://img0.ph.126.net/lzi5S3r6CZCsDc5B2vojTA==/6608630031911566776.png" />是<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />的一个解

B、<img src="http://img1.ph.126.net/NISek9ewKLCHG1fEN6NCUw==/6630196952491411213.png" />是<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />的一个解

C、<img src="http://img1.ph.126.net/mx-TZP1bYGXkq17Qp8Jhaw==/653584895940257767.png" />是<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />的一个解

D、<img src="http://img1.ph.126.net/HY1rOOVDkIEojnAG2Khxcg==/3838192782526671856.png" />是<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />的一个解

15、【多选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img1.ph.126.net/4lvv3F3qRcxYtenGSXQ67w==/6630537801095362288.png" />矩阵，<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />是非齐次线性方程组<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />所对应的齐次线性方程组，则下列结论错误的是（）.

A、若<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />只有零解，则<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />有唯一解

B、若<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />有非零解，则<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />有无穷多解

C、若<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />有无穷多解，则<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />只有零解

D、若<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />有无穷多解，则<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />有非零解

16、【多选题】设<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是正交矩阵，则下列结论正确的是（）.

A、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的转置仍然是正交矩阵

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的逆矩阵等于<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的转置矩阵

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个行向量构成一组规范正交基

D、单位矩阵<img src="http://img2.ph.126.net/819ljKUveipB7sYvOvFlwQ==/6608769669887245088.png" />不是正交矩阵

17、【判断题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是一个方阵，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" style="white-space: normal;" />的行空间<img src="http://img1.ph.126.net/3GNEvpRkf3PrGxNJcTkRvQ==/6631262379262934233.png" />中的向量与其零空间<img src="http://img0.ph.126.net/d9AEm8seMQihPxGUC2V5gw==/6630868754096638302.png" />中的向量是正交的.

A、正确

B、错误

18、【判断题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" style="white-space: normal;" />是一个方阵，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" style="white-space: normal;" />的列空间<img src="http://img1.ph.126.net/OtyocC2RR8T8C-FjMv1v1A==/6630841266305941342.png" />中的向量与其零空间<img src="http://img0.ph.126.net/d9AEm8seMQihPxGUC2V5gw==/6630868754096638302.png" style="white-space: normal;" />中的向量是正交的.

A、正确

B、错误

19、【判断题】设<img src="http://img0.ph.126.net/ohfMIFH44HORvasXTiYCqg==/6599281984052422974.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />元单位列向量, 那么<img src="http://img0.ph.126.net/HAB9jOmnnFTvMD2rBe8qGQ==/6631248085611771354.png" />是正交矩阵.

A、正确

B、错误

20、【判断题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵，则<img src="http://img2.ph.126.net/6UeZsXMRnx04gjGAHcIVkA==/1136033006021716061.png" />是<img src="http://img2.ph.126.net/K-1gCGUz5NEjD2f8PDzBkA==/6598089013996132115.png" />的展开式中的一项.

A、正确

B、错误

第六周单元测验

1、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是一个方阵, 则下列命题正确的是（）.

A、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的某一行的倍数加到另一行上得到矩阵<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />, 那么<img src="http://img1.ph.126.net/ISeBG7sZblvoFhzSSgE3vw==/6631447097212157563.png" />.

B、如果互换<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的两行得到矩阵<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />, 那么<img src="http://img1.ph.126.net/ISeBG7sZblvoFhzSSgE3vw==/6631447097212157563.png" />.

C、如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的某一行乘以<img src="http://img2.ph.126.net/gb-5yiJlO7MTtzp8_5MwmQ==/6608425522748584130.png" />倍得到矩阵<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />, 那么<img src="http://img1.ph.126.net/e6ghcXfV5AZ_LXK8lR3wvg==/6631228294398207961.png" />.

D、三角形矩阵的行列式等于它的主对角元之和

2、【单选题】<img src="http://nos.netease.com/edu-image/763B671F3A60776A1CE3E602E205E391.png?imageView

A、<img src="http://img2.ph.126.net/NPS3RCgLj1737c5r9jcOPA==/6631273374374946812.png" />

B、<img src="http://img2.ph.126.net/ybGfq7wBMhAykL2sZpSdyA==/6631246986095863781.png" />

C、<img src="http://img0.ph.126.net/Sw7KPboTrZpFOi6lB-Vpew==/6631273374374946849.png" />

D、<img src="http://img2.ph.126.net/xl8bogOId-RgWR_HiUOboQ==/6631301961677271758.png" />

3、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是一个方阵, 则下列命题正确的是（）.

A、若对<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />连续作两次行的交换, 则得到的矩阵的行列式等于<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行列式

B、若<img src="http://img0.ph.126.net/zjRomtrFy-TP-2yItaubTA==/6631252483654002879.png" />, 则其两行或两列相同, 或者一行或一列为零

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的转置的行列式等于<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行列式的负值

D、方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行列式等于它的主对角元之积

4、【单选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" /> 均为4阶方阵. 如果<img src="http://img2.ph.126.net/daZavvWhxr8JLG7rlyb50w==/6631339345072605101.png" />, <img src="http://img1.ph.126.net/7d95VayjPtCTYdCJNMJTzw==/6631403116747020007.png" /> 那么（）.

A、<img src="http://img2.ph.126.net/b_mnrYaskmMSnD9OWnEvdA==/6631336046537721938.png" />

B、<img src="http://img1.ph.126.net/lelGFtZSx2fvqsN5LrOIYg==/6631216199770299892.png" />

C、<img src="http://img1.ph.126.net/4mFo3HMqW8fh_-93tlP2Hg==/6631391022119118034.png" />

D、<img src="http://img1.ph.126.net/XYGHGtyj3Ekk8KUd2YcuvQ==/6631404216258647842.png" />

5、【单选题】下列命题正确的是（）.

A、若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为2阶矩阵, 并且<img src="http://img0.ph.126.net/zjRomtrFy-TP-2yItaubTA==/6631252483654002879.png" />, 则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的一列是另一列的倍数

B、若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为3阶矩阵, 则<img src="http://img1.ph.126.net/DgX2dhPh_UI82dsZY7PGvQ==/6631424007467949523.png" />

C、若<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵, 且<img src="http://img2.ph.126.net/mbyDE4ARkMV2MW5vHA_4iw==/6631421808444694076.png" />, 则<img src="http://img2.ph.126.net/xEbCr0Dl5yp-MHcRyVxqUw==/6631251384142375631.png" />

D、<img src="http://img0.ph.126.net/Z82cQzWvyy2PVTaL_tPp4A==/6631317354840058689.png" />

6、【单选题】<img src="http://nos.netease.com/edu-image/20752DD7B5133C72766C85C0C78EBF3F.png?imageView

A、<img src="http://img2.ph.126.net/fqWbciXp1Cr2VFmjTMMDBw==/6631214000747044835.png" />

B、<img src="http://img1.ph.126.net/4xQceX2bvSdjj-Sw_qenlA==/6631387723584235168.png" />

C、<img src="http://img0.ph.126.net/acVV98YWaLkZdmKgMI39JA==/6619542684817347447.png" />

D、<img src="http://img2.ph.126.net/jEceH01Qa2hDXh_H263eKQ==/978969969016517405.png" />

7、【单选题】已知4阶行列式的值为92, 它的第2行元素依次为1, 0, <img src="http://img1.ph.126.net/VNFztsVinaRqNakA9kMAgA==/3096787693788755425.png" />, 2, 且第2行元素的余子式分别为1, 3, <img src="http://img0.ph.126.net/eL8MWiNlujHx04qlduEsCw==/3838192782527135538.png" />, 2, 则<img src="http://img1.ph.126.net/91UQhB5nxxSdGH8DVOIrOg==/6630104593513509133.png" />（）.

A、<img src="http://img0.ph.126.net/tc1G25MaH50XKzGSQwDpxQ==/2763521321363221779.png" />

B、<img src="http://img1.ph.126.net/9jNB8QyS0IoIBM9EMEL9GQ==/53198770616413807.png" />

C、<img src="http://img0.ph.126.net/y4FcHeJrqGu4Bp6FncKJyQ==/2448550822424389419.png" />

D、<img src="http://img1.ph.126.net/lTOReMeobMnsxT827DN1gw==/3112550292484716865.png" />

8、【单选题】已知<img src="http://img2.ph.126.net/mwU_yZTj1MfxE1RqnNsI7A==/6608555265120376937.png" />为<img src="http://img1.ph.126.net/vQs7qNG27PRvjguKUs8RJQ==/1139410705825568242.png" />阶方阵，<img src="http://img0.ph.126.net/bqUyoYe1VFpg6OHTfcddKQ==/62487444847709187.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵，则 <img src="http://img1.ph.126.net/RsRxOqF1aiwtio4lrYM_iw==/6631268976328486180.png" />

A、<img src="http://img1.ph.126.net/GDusl6DDg7r95-ZDD84hnQ==/1357835287670334175.png" />

B、<img src="http://img2.ph.126.net/sBp4iaigv7WDrQ4kkwAANg==/6630810479980507361.png" />

C、<img src="http://img1.ph.126.net/eAED79oz_dK1iz597A3jvg==/6630696130771225033.png" />

D、<img src="http://img1.ph.126.net/ElmOepJrGR_oYBO9GRlZcw==/2507942042510068900.png" />

9、【单选题】<img src="http://nos.netease.com/edu-image/F148B2F40B585027D93A0AB022FBDEE8.png?imageView

A、<img src="http://img2.ph.126.net/H4AHN3nFxX8TlMOVESG9Aw==/2998552926999113081.png" />

B、<img src="http://img0.ph.126.net/hk3BNsCLjOzKLIDOFvYKiA==/6599309471843160411.png" />

C、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

D、<img src="http://img0.ph.126.net/IkxMY9N1n18bExa2LUs7ug==/6608646524584900572.png" />

10、【单选题】<img src="http://nos.netease.com/edu-image/8F9A0C6982CFD18A121A7A7DD618C6AD.png?imageView

A、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

B、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

C、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

D、<img src="http://img0.ph.126.net/syWk7sgCWzxHuJrCGNHgpQ==/6608551966585017441.png" />

11、【单选题】<img src="http://nos.netease.com/edu-image/E67D9F335764E7B28592432BCB0ABAA2.png?imageView

A、<img src="http://img0.ph.126.net/syWk7sgCWzxHuJrCGNHgpQ==/6608551966585017441.png" />

B、<img src="http://img1.ph.126.net/Sm322J8AbwodTOMWXp_llA==/6619300792259364523.png" />

C、<img src="http://img2.ph.126.net/lzN7yR-lhsq0E4UP2yHxlQ==/1124211057000459866.png" />

D、<img src="http://img2.ph.126.net/UOkA-xWvJqXiDUFYxP-UPQ==/4872894796915134680.png" />

12、【单选题】<img src="http://nos.netease.com/edu-image/93A0D8FFFEE936A969FB947EE9AACCA4.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img1.ph.126.net/EPqERM2i2imijqbHeLl5Zw==/2447706397492657318.png" />

B、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

C、<img src="http://img0.ph.126.net/IkxMY9N1n18bExa2LUs7ug==/6608646524584900572.png" />

D、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

13、【单选题】设<img src="http://img2.ph.126.net/oLWtU3SZj_B1NzVYcASvTg==/1020628265570947139.png" />,<img src="http://img1.ph.126.net/9zepWlKiyfPt0BJA07oBUA==/2444610172750432651.png" />是4阶方阵, 且<img src="http://img0.ph.126.net/1KYT9murLrk0bGYH4YDGtQ==/6608539871958095607.png" />,则<img src="http://img1.ph.126.net/ewDxg46gTjWlLMtCGWOOHA==/6631266777305187751.png" />（）.

A、<img src="http://img0.ph.126.net/U3SnEcPQdBkv53cW44jA6A==/3357714997282665399.png" />

B、<img src="http://img2.ph.126.net/jkpaPy_zAokYqW8qJeFisQ==/6619384355142185462.png" />

C、<img src="http://img2.ph.126.net/hosf37-sNaNufMwCaYh_Fw==/6608259496492814132.png" />

D、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

14、【单选题】<img src="http://nos.netease.com/edu-image/EA0423586D56DCDE32F4D179151C8E8F.png?imageView

A、<img src="http://img0.ph.126.net/hk3BNsCLjOzKLIDOFvYKiA==/6599309471843160411.png" />

B、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

C、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

D、<img src="http://img0.ph.126.net/syWk7sgCWzxHuJrCGNHgpQ==/6608551966585017441.png" />

15、【单选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />都是3阶方阵，且<img src="http://img1.ph.126.net/mlQ1josPdWmnX-h4lnqqkQ==/6631237090491282436.png" />则<img src="http://img2.ph.126.net/8D5cIsvYGx3FCKfLABy7-g==/6631210702212212027.png" />

A、<img src="http://img1.ph.126.net/pMzmWUqhFkf2B8MdBxwhVg==/6631209602700583597.png" />

B、<img src="http://img1.ph.126.net/YMCp8EIiwu5YfFSemNFKLw==/887490601669039159.png" />

C、<img src="http://img2.ph.126.net/VtnRFDEUGakLUkTmMpoAwA==/6608557464143058506.png" />

D、<img src="http://img0.ph.126.net/Eq-eiZ_ShWGeYJwxHtMNsQ==/6631328349956384790.png" />

16、【多选题】设 <img src="http://img2.ph.126.net/g1wp8jhB7nDOYXsJLfZyHA==/6630828072166520237.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵, <img src="http://img2.ph.126.net/46_kHRcEU0sY6JCAP5cPrg==/1058345912449014257.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的伴随矩阵. 如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />可逆, 则以下各式正确的是（）.

A、<img src="http://img1.ph.126.net/wFWiCz6D27oNDApir10AWA==/1180506052342774129.png" />

B、<img src="http://img0.ph.126.net/ptpV3xP2qBrevjwW0Wb3PA==/1040894463894252231.png" />

C、<img src="http://img1.ph.126.net/FGbp-q4YOrOVNTOjGWEnSw==/2771965570664653729.png" />

D、<img src="http://img2.ph.126.net/Vsk4JKVmDyOlbOuZuHrzEA==/6619585565770956938.png" />

17、【多选题】设 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵. 如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是非奇异的, 则下列说法正确的为（）.

A、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />一定可逆‍

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的秩等于<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />

C、<img src="http://img2.ph.126.net/mvhqBqV69NR0kiJ7vJ3d7g==/6630845664352524971.png" />一定有解

D、<img src="http://img2.ph.126.net/MK5hQhiGpQRPiFmYMN4IMg==/6608513483678739449.png" />有非零解

18、【判断题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" style="color: rgb(0, 0, 0); font-family: Arial, 'Hiragino Sans GB', 'Microsoft YaHei', 微软雅黑, Helvetica, sans-serif; font-size: 16px; line-height: 26px; white-space: pre-wrap;" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" style="color: rgb(0, 0, 0); font-family: Arial, 'Hiragino Sans GB', 'Microsoft YaHei', 微软雅黑, Helvetica, sans-serif; font-size: 16px; line-height: 26px; white-space: pre-wrap;" />阶方阵, 如果<img src="http://img0.ph.126.net/N6kmUdNWlz-sAnbVpmSWhQ==/6598248443182258323.png" />, 那么<img src="http://img0.ph.126.net/XSkgq7261U3BEVaAIm6eNQ==/3355463197469027979.png" />.

A、正确

B、错误

19、【判断题】如果方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的行向量组是线性相关的, 那么<img src="http://img1.ph.126.net/Ozdp5L9Mbzd_9FBGamwdOg==/6630430048956497887.png" />.

A、正确

B、错误

20、【判断题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵, 如果<img src="http://img2.ph.126.net/KvLZGcPPGoqtedyF8r9H2w==/6598063725228977990.png" />, 那么<img src="http://img0.ph.126.net/XSkgq7261U3BEVaAIm6eNQ==/3355463197469027979.png" />.

A、正确

B、错误

第七周单元测验

1、【单选题】<img src="http://nos.netease.com/edu-image/E9B43C50E449B39B73BC893F8B461718.jpg?imageView

A、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

B、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

C、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

D、<img src="http://img2.ph.126.net/hosf37-sNaNufMwCaYh_Fw==/6608259496492814132.png" />

2、【单选题】若<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的任意一行中<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个元素的和都是<img src="http://img1.ph.126.net/knoGV4UX9L4YUquOIP-Jxw==/1409626683467679913.png" />，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的一个特征值为（）.

A、<img src="http://img1.ph.126.net/knoGV4UX9L4YUquOIP-Jxw==/1409626683467679913.png" />

B、<img src="http://img1.ph.126.net/Y7wKEaGGeNBuSwc9GbYuyg==/6608251799912132017.png" />

C、<img src="http://img0.ph.126.net/syWk7sgCWzxHuJrCGNHgpQ==/6608551966585017441.png" />

D、<img src="http://img1.ph.126.net/dRPZXOgppdUdS-YoYcSEkQ==/6619129268445155020.png" />

3、【单选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶可逆矩阵，<img src="http://img1.ph.126.net/YCPyo8OH0kQUkwq71yxhtA==/6608514583189659373.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的一个特征值，则<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的伴随矩阵<img src="http://img2.ph.126.net/46_kHRcEU0sY6JCAP5cPrg==/1058345912449014257.png" />的特征值之一是（）.

A、<img src="http://img0.ph.126.net/hmKYsg5DY84ulKKahczB2Q==/6608540971469729292.png" />

B、<img src="http://img2.ph.126.net/oZ06gafQZpDw5Ho7IzPOrA==/6619259010817516340.png" />

C、<img src="http://img1.ph.126.net/iXqieah8N4u-jotCx1DY8g==/6619157855747765377.png" />

D、<img src="http://img1.ph.126.net/5sK_W855myWi1kGeBJ0uCg==/1168402628344105165.png" />

4、【单选题】若 <img src="http://img1.ph.126.net/3C1vspvZuJuRDYfmQ8RvUQ==/6608764172330168359.png" />，则有（）.

A、<img src="http://img2.ph.126.net/tMXGoWwYDj2-a7-DhKAcew==/1105070758584122423.png" />

B、<img src="http://img1.ph.126.net/jlAn1Gutc9b8ADcVZir_cA==/2870200337537047561.png" />

C、对于相同的特征值<img src="http://img1.ph.126.net/YCPyo8OH0kQUkwq71yxhtA==/6608514583189659373.png" />，矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />有相同的特征向量

D、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />均与同一个对角矩阵相似

5、【单选题】<img src="http://nos.netease.com/edu-image/64ECFA1E3FB5EE47C02FE8D8F49F6F5D.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

B、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

C、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

D、<img src="http://img2.ph.126.net/Qmrmc7fo2KzgJyO-CkfG3g==/4841651074500465896.png" />

6、【单选题】<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个不同的特征值这一论断是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与对角矩阵相似的（）.

A、充分而非必要条件

B、充分必要条件

C、必要而非充分条件

D、既非充分也非必要条件

7、【单选题】<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与对角矩阵相似的充分必要条件是（）.

A、 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有个<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />线性无关的特征向量

B、 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个不全相等的特征值

C、 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有个<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />不相同的特征向量

D、 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个全不相同的特征值

8、【单选题】<img src="http://nos.netease.com/edu-image/652CF18E24B96FEBD229033170F87095.png?imageView&thumbnail=520x520&quality=100" />

A、<img src="http://img1.ph.126.net/JUA51m2ayqp54-2j-hsMsQ==/841328705488419067.png" />

B、<img src="http://img1.ph.126.net/QgcXKR-HWkemQz-tl77Jrg==/723390690246721792.png" />

C、<img src="http://img0.ph.126.net/hk3BNsCLjOzKLIDOFvYKiA==/6599309471843160411.png" />

D、<img src="http://img1.ph.126.net/avDefb1ml7mGtLfMPsP-Uw==/1677027911342356792.png" />

9、【单选题】<img src="http://nos.netease.com/edu-image/40D1FB742C97AFE65D23A001A960A43F.png?imageView

A、<img src="http://img0.ph.126.net/WUEfXMfsJOAunqzH3MhuZg==/3670152221430749034.png" />

B、<img src="http://img2.ph.126.net/Qmrmc7fo2KzgJyO-CkfG3g==/4841651074500465896.png" />

C、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

D、<img src="http://img2.ph.126.net/1CmlhCQWG9IrSasZ3FJ27A==/2855563638830699306.png" />

10、【单选题】已知一个三阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />可以相似对角化, 2是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的一个二重特征值,则<img src="http://img1.ph.126.net/qs11Bi5v1QPadwJ9FXCcXw==/6630781892678214703.png" />的基础解系里含有（）个向量?

A、<img src="http://img0.ph.126.net/oGeVumerm5nFB_acqunIrQ==/4787889353948587071.png" />

B、<img src="http://img1.ph.126.net/Z0cPG2fLoo6myX8ArxXy5g==/4848687948918187486.png" />

C、<img src="http://img2.ph.126.net/6fXIZVJ5n9swpT9pjlIZBQ==/6608207819446238675.png" />

D、<img src="http://img2.ph.126.net/hosf37-sNaNufMwCaYh_Fw==/6608259496492814132.png" />

11、【单选题】若3阶矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />相似于<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />, 矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的特征值是<img src="http://img2.ph.126.net/CZSDiKJYto_9zr4pW_Mpdg==/6631430604537325433.png" />, 那么行列式<img src="http://img2.ph.126.net/I5o7ZAEyUa5_OIu3W2ERHQ==/983192093668881026.png" />（）.

A、<img src="http://img0.ph.126.net/GuBnTHcYW-O9rpH2Kdeg6Q==/6630648851769593325.png" />

B、<img src="http://img2.ph.126.net/1CmlhCQWG9IrSasZ3FJ27A==/2855563638830699306.png" />

C、<img src="http://img0.ph.126.net/Ne0SH_c9ILc3XLjRYU1TXA==/2211267417140003805.png" />

D、<img src="http://img2.ph.126.net/7YwWfAdC0TAZ17SMcLxE2g==/6630327794374347128.png" />

12、【单选题】n阶矩阵<img src="http://img1.ph.126.net/3C1vspvZuJuRDYfmQ8RvUQ==/6608764172330168359.png" />的充分条件是（）.

A、 <img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />均与对角矩阵<img src="http://img1.ph.126.net/_-ks4W97B7zRTcclrTE3nQ==/6608701500166779562.png" />相似

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />有相同的特征值

C、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />有相同的特征向量

D、<img src="http://img1.ph.126.net/-9AsGjH2s1E9rioPP8DbJQ==/2779846870011957568.png" />与<img src="http://img2.ph.126.net/65tmpKiUBkXNmA15Z8rEaw==/6630752205862656929.png" />相似

13、【多选题】设<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />是<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，<img src="http://img2.ph.126.net/Dbsw_tbYLUgLtI_kI7qKCw==/6597745966309635401.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的特征值，<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的分别对应于<img src="http://img2.ph.126.net/Dbsw_tbYLUgLtI_kI7qKCw==/6597745966309635401.png" />的特征向量，则下列说法错误的是（）.

A、 <img src="http://img2.ph.126.net/RfboT1HaNDafLUHBUVzkdQ==/2287547135828544671.png" />时，<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />一定成比例

B、 <img src="http://img2.ph.126.net/RfboT1HaNDafLUHBUVzkdQ==/2287547135828544671.png" />时，<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />一定不成比例

C、 <img src="http://img0.ph.126.net/eQYVRVMTrqVa2YVZ4fGMmQ==/6631257981212434698.png" />时，<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />一定成比例

D、 <img src="http://img0.ph.126.net/eQYVRVMTrqVa2YVZ4fGMmQ==/6631257981212434698.png" />时，<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />一定不成比例

14、【多选题】<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />相似于对角矩阵，则下列不正确的是（）.

A、方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的秩等于<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />

B、方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />有<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />个不同的特征值

C、方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />一定是对称阵

D、方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />任意特征值的代数重数和几何重数都相等

15、【多选题】设<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶矩阵，且<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />相似，<img src="http://img2.ph.126.net/819ljKUveipB7sYvOvFlwQ==/6608769669887245088.png" />为<img src="http://img2.ph.126.net/X0i4IOwGUEH1WFhLROWTyg==/6608898312747659924.png" />阶单位矩阵，则下列说法正确的是（）.

A、<img src="http://img0.ph.126.net/SRaMWLN0N_l1vmEPe6FyFA==/6630762101468913651.png" />

B、<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />与<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />有相同的特征值

D、对任意常数t，<img src="http://img2.ph.126.net/YioadTcm-WKNfD2dZcJkYg==/6631383325538013161.png" />与<img src="http://img0.ph.126.net/sbnyjc19VPeA-ua7ipLndQ==/6631316255328710067.png" />相似

16、【判断题】设<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />是矩阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的属于不同特征值的特征向量, 则<img src="http://img1.ph.126.net/UtK-lZE3f4fkJ2SJHfxqkw==/6598136292996401533.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的特征向量.

A、正确

B、错误

17、【判断题】方阵<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />不可逆的充分必要条件为零是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的一个特征值.

A、正确

B、错误

18、【判断题】如果<img src="http://img2.ph.126.net/pSq6wL38wviMw6O_OinFkQ==/6630202450048291280.png" />是<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的线性无关的特征向量, 那么它们一定属于<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />的不同特征值.

A、正确

B、错误

19、【判断题】如果<img src="http://img1.ph.126.net/4QRI30JkP7V6jj57tHynuQ==/6608641027026760798.png" />相似于<img src="http://img2.ph.126.net/KI6l_Ha2xYY45m9QKSmL8g==/6608229809678832062.png" />, 那么<img src="http://img1.ph.126.net/jlAn1Gutc9b8ADcVZir_cA==/2870200337537047561.png" />，其中<img src="http://img1.ph.126.net/YCPyo8OH0kQUkwq71yxhtA==/6608514583189659373.png" />为<img src="http://img1.ph.126.net/9Jp9tyt6qP7_Cms5bNCYQA==/6608609141189555956.png" />的一个特征值.

A、正确

B、错误