西交《线性代数》在线作业

adminhan

&nbsp;<img width="573" height="133" alt="" src="http://file.open.com.cn/ItemDB/126539/1792cd11-ff19-478f-b8bd-d238872ec52a/2015513212426322.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="535" height="101" alt="" src="http://file.open.com.cn/ItemDB/201621133826822.png" />
A:A
B:B
C:C
D:D

设向量组a1,a2,a3线性无关,则下列向量组中线性无关的是(     )。
A:a1-a2,a2-a3,a3-a1
B:a1,a2,a3+a1
C:a1,a2,2a1-3a2
D:a2,a3,2a2+a3

&nbsp;<img width="548" height="114" alt="" src="http://file.open.com.cn/ItemDB/126539/d389e9c0-41d8-48c0-b94e-3bacaf7401d0/201551321313440.jpg" />
A:A
B:B
C:C
D:D

n阶矩阵A相似于对角矩阵的充分必要条件是(   )
A:A有n个互不相同的特征向量.
B:A有n个线性无关的特征向量.
C:A有n个两两正交的特征向量.
D:A有n个互不相同的特征值.

&nbsp;<img width="627" height="110" alt="" src="http://file.open.com.cn/ItemDB/126539/22ba730e-56e2-4323-8778-d2f0bdfd4dfa/2016211350520.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="705" height="151" alt="" src="http://file.open.com.cn/ItemDB/126539/4b43e669-d077-4ac8-93c5-30cc9e22fd53/201621134842525.png" />
A:A
B:B
C:C
D:D

&nbsp; <img width="487" height="182" alt="" src="http://file.open.com.cn/ItemDB/126539/22ba730e-56e2-4323-8778-d2f0bdfd4dfa/201621135019270.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="578" height="98" alt="" src="http://file.open.com.cn/ItemDB/126539/2ef36c94-1ef1-4f58-844d-dd052c1f2fc0/201551321319750.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="530" height="61" alt="" src="http://file.open.com.cn/ItemDB/126539/458597bd-6832-4012-aa09-fe830f6aebe4/2015513212444777.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="507" height="118" alt="" src="http://file.open.com.cn/ItemDB/2015513213213861.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="470" height="108" alt="" src="http://file.open.com.cn/ItemDB/126539/4b43e669-d077-4ac8-93c5-30cc9e22fd53/20162113493491.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="625" height="104" alt="" src="http://file.open.com.cn/ItemDB/126539/22ba730e-56e2-4323-8778-d2f0bdfd4dfa/20162113434234.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="536" height="114" alt="" src="http://file.open.com.cn/ItemDB/126539/1075b5b9-0f5b-4c18-90a8-e3b47a013d33/2015513212523636.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="407" height="134" alt="" src="http://file.open.com.cn/ItemDB/126539/5cc885e7-3fc9-4469-aa50-51089bb7f6ea/20162113428831.png" />
A:A
B:B
C:C
D:D

&nbsp;<img alt="" width="415" height="141" src="http://file.open.com.cn/ItemDB/126539/ee13f884-4f04-454a-8c01-e455321f81bb/2015513212244674.jpg" />
A:A
B:B
C:C
D:D

&nbsp; <img alt="" width="587" height="105" src="http://file.open.com.cn/ItemDB/20162113442940.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="417" height="106" alt="" src="http://file.open.com.cn/ItemDB/126539/b99c3d76-2562-4f4f-a36e-836cd51bfc25/2015513213252378.jpg" />
A:A
B:B
C:C
D:D

设λ0是矩阵A的特征方程的3重根,A的属于λ0的线性无关的特征向量的个数为k,则必有(    )
A:k≤3
B:k<3
C:k=3
D:k>3

&nbsp;<img width="580" height="151" alt="" src="http://file.open.com.cn/ItemDB/126539/47761181-ff74-4618-a37b-5de662d33839/2015513212819901.jpg" />
A:A
B:B
C:C
D:D

设u1, u2是非齐次线性方程组Ax = b的两个解,若c1u1+c2u2也是方程组Ax = b的解,则(   ).
A:c1+c2 =1
B:c1= c2
C:c1+ c2 = 0
D:c1= 2c2

&nbsp;<img width="480" height="157" alt="" src="http://file.open.com.cn/ItemDB/126539/2ab32583-44b0-4ead-a8cb-679e02aa2c30/2015513212649608.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="619" height="70" alt="" src="http://file.open.com.cn/ItemDB/126539/4b43e669-d077-4ac8-93c5-30cc9e22fd53/201621134810778.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="568" height="167" alt="" src="http://file.open.com.cn/ItemDB/126539/a238dcdf-3e88-48a3-b289-9050cf8c512a/201551321298288.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="522" height="302" alt="" src="http://file.open.com.cn/ItemDB/201621121645513.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="606" height="92" alt="" src="http://file.open.com.cn/ItemDB/201621134826736.png" />
A:A
B:B
C:C
D:D

设A为m*n矩阵,则有( &nbsp; &nbsp; &nbsp;)
A:若m&lt;n，则有Ax=b无穷多解
B:若m&lt;n，则有Ax=0非零解，且基础解系含有n-m个线性无关解向量
C:若A有n阶子式不为零，则Ax=b有唯一解
D:若A有n阶子式不为零，则Ax=0仅有零解。

设A,B均为n阶非零方阵,下列选项正确的是(   ).
A:(A+B)(A-B) = A^2-B^2
B:(AB)^-1 = B^-1A^-1
C:若AB= O, 则A=O或B=O
D:|AB| = |A| |B|

&nbsp;<img width="580" height="152" alt="" src="http://file.open.com.cn/ItemDB/126539/8fecf747-2457-45d7-a107-c6e2b3b31762/2015513212743896.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="637" height="111" alt="" src="http://file.open.com.cn/ItemDB/126539/db93b49f-e150-4b59-9de6-ec75d308b837/201621134246117.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="699" height="102" alt="" src="http://file.open.com.cn/ItemDB/126539/0a94f7cb-2be3-4c40-b7e6-4199281b5cf3/20162113397929.png" />
A:A
B:B
C:C
D:D

&nbsp;<img width="568" height="155" alt="" src="http://file.open.com.cn/ItemDB/2015513212936553.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="569" height="123" alt="" src="http://file.open.com.cn/ItemDB/126539/6c83e01a-b834-453e-847c-70253584babc/2015513213026693.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="575" height="110" alt="" src="http://file.open.com.cn/ItemDB/126539/43bb4b95-c65f-4421-9148-caedd5ff5809/201551321300266.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="516" height="124" alt="" src="http://file.open.com.cn/ItemDB/126539/2ecc71ae-81dc-4d45-8741-014f7172f061/201551321276799.jpg" />
A:A
B:B
C:C
D:D

&nbsp;<img width="558" height="34" alt="" src="http://file.open.com.cn/ItemDB/126539/b205156a-8f55-422c-8e46-d84ec51887e7/201621135247958.png" />
A:错误
B:正确

&nbsp;<img width="591" height="44" alt="" src="http://file.open.com.cn/ItemDB/126539/16112259-d0b0-4bf2-a2f8-cd0ce57a1425/201621135646404.png" />
A:错误
B:正确

&nbsp;<img width="485" height="32" alt="" src="http://file.open.com.cn/ItemDB/126539/5bdffdba-7ab7-489a-9fd5-7e6e0d58d656/2015513213818668.jpg" />
A:错误
B:正确

&nbsp;<img width="549" height="45" alt="" src="http://file.open.com.cn/ItemDB/126539/6037ff01-f406-4228-bf57-fba788fe2601/20162113560544.png" />
A:错误
B:正确

&nbsp;<img width="345" height="26" alt="" src="http://file.open.com.cn/ItemDB/126539/57e51598-0b24-429f-8ad7-b2ed0e18c841/2015513213745237.jpg" />
A:错误
B:正确

&nbsp;<img width="584" height="69" alt="" src="http://file.open.com.cn/ItemDB/126539/d71704f7-bb6c-4873-a3e5-4a8db63d9c25/2015513213939159.jpg" />
A:错误
B:正确

&nbsp;<img width="291" height="91" alt="" src="http://file.open.com.cn/ItemDB/126539/557898fe-2a80-47e3-8903-25e6d8d203f8/201621135417134.png" />
A:错误
B:正确

&nbsp;<img width="543" height="35" alt="" src="http://file.open.com.cn/ItemDB/126539/daaad730-ce84-420c-8a6c-0d4b620f11e7/2015513213834362.jpg" />
A:错误
B:正确

设6阶方阵A的秩为3,则其伴随矩阵的秩也是3。
A:对
B:错

&nbsp;<img width="664" height="76" alt="" src="http://file.open.com.cn/ItemDB/126539/ab9725a5-9fea-4607-adf2-49dfe18d1161/201621135449299.png" />
A:错误
B:正确

&nbsp;<img width="281" height="31" alt="" src="http://file.open.com.cn/ItemDB/126539/157d404b-22d6-47c2-94c6-468a56c2423c/2015513213633975.jpg" />
A:错误
B:正确

&nbsp;<img width="432" height="42" alt="" src="http://file.open.com.cn/ItemDB/126539/04bfe917-ce5a-45d5-974f-91436bf83d4c/20162113523477.png" />
A:错误
B:正确

&nbsp;<img width="510" height="48" alt="" src="http://file.open.com.cn/ItemDB/126539/798a3b8a-91cd-4aa1-907f-706a8e11ff2d/201621135512148.png" />
A:错误
B:正确

四阶行列式D中第3列元素依次为 -1,2,0,1,它们的余子式的值依次为5,3,-7,4,则D = -10 .
A:对
B:错

&nbsp;<img width="655" height="45" alt="" src="http://file.open.com.cn/ItemDB/126539/557898fe-2a80-47e3-8903-25e6d8d203f8/201621135316198.png" />
A:错误
B:正确