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1、1 数学系高等代数期末考试试卷年级专业学号姓名注：考试时间 120 分钟，试卷满分 100 分。题号一二三四五总分签 名得分一得 分阅卷教师一判断题（正确的在题后的括号内打“”；错误的在题后的括号内打“”.每小题 2 分，共 18 分）1向量空间一定含有无穷多个向量.()2若向量空间 V 的维数2dimV,则V 没有真子空间.()3.n维向量空间中由一个基到另一个基的过渡矩阵必为可逆矩阵.()4线性变换把线性无关的向量组映成线性无关的向量组.()5每一个线性变换都有本征值.()6 若向量是线性变换的属于本征值的本征向量，则由生成的子空间为的不变子空间.()7保持向量间夹角不变的线性变换是正交变
2、换.()8两个复二次型等价的充分必要条件是它们有相同的秩.()9.若两个n阶实对称矩阵BA,均正定,则它们的和BA也正定.()二得分阅卷教师二单项选择题（在每小题的四个备选答案中，选出一个正确的答案，并将其号码填在题目的括号内.每小题 2 分，共 10分）1.下列命题不正确的是 ().A.若向量组,21r线性无关，则它的任意一部分向量所成的向量组也线性无关；B.若向量组,21r线性相关，则其中每一个向量都是其余向量的线性组合；C.若向量组,21r线性无关，且每一i可由向量,21s线装订线2 性表示，则sr；D.)0(nn维向量空间的任意两个基彼此等价.2.下列关于同构的命题中，错误的是().A
3、向量空间 V 的可逆线性变换是 V 到 V 的同构映射；B 数域 F 上的n维向量空间的全体线性变换所成向量空间与数域F上的所有n阶矩阵所成向量空间同构；C若是数域 F 上向量空间 V 到W 的同构映射，则1是W到V 的同构映射；D向量空间不能与它的某一个非平凡子空间同构.3n阶矩阵 A有n个不同的特征根是A与对角矩阵相似的 ().A充分而非必要条件；B 必要而非充分条件；C充分必要条件；D.既非充分也非必要条件4二次型21213211312),(),(xxxxxxxq的矩阵是().A1312；B1112；C 000013013；D0000110125.实二次型Axxxxxq),(321正定的
4、充分且必要条件是 ().A0A；B秩为 3；C A合同于三阶单位矩阵；D 对某一,0),(321xxxx有0Axx.三得 分阅卷教师三填空题（每小题2 分，共 10 分，把答案填在题中横线上）1.复数域C作为实数域R上的向量空间，它的一个基是_.2.设,2,1,),(21niFxxxxFinn是数域F上n元行空间，对任意nnFxxx),(21，定义),0,0(),(22121nnxxxxxx，则是一个线性变换，且的核)(Ker的维数等于 _.3.若A是一个正交矩阵，则2A的行列式2A=_.文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C
5、3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6
6、E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q
7、6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L1
8、0C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8
9、C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E
10、6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1
11、L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F93 4.在欧氏空间3R中向量)0,0,1(1与)0,1,0(2的夹角=_.5.实数域上5元二次型可分为 _类，属于同一类的二次型彼此等价，属于不同类的二次型互不等价.四得分阅卷教师四计算题（每小题 14 分，共 42 分）1求齐次线性方程组033450220230432143243214321xxxxxxxxxxxxxxx的解空间的一个基，再进一步实施正交化，求出规范
12、正交基2设230120001A,求 A的特征根及对应的特征向量.问 A是否可以对角化？若可以，则求一可逆矩阵T，使ATT1为对角形.文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5
13、 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文
14、档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K
15、7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3
16、R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F
17、9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C
18、3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F94 3 写出 3 元二次型32213214),(xxxxxxxq的矩阵试用非奇异的线性变换，将此二次型变为只含变量的平方项.五得 分
19、阅卷教师文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L
20、10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B
21、8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1
22、E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF
23、1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA
24、1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7
25、S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F95 五证明题（每小题10 分，共 20 分）1设21,为n阶矩阵 A的属于不同特征根，21,分别是 A的属于21,的特征向量，证明21不是 A的特征向量.2设是n维欧氏空间 V 的正交变换，且2为单位变换，A是关于 V 的某一规范正交基的矩阵，证明A为对称
26、矩阵文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10
27、C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C
28、6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6
29、Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L
30、10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B
31、8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1
32、E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F96 数学系高等代数期末考试试卷（A 卷）年级专业学号姓名注：考试时间 120 分钟，试卷满分 100 分。题号一二三四五总分签 名得分一得 分阅卷教师一判断题（正确的在题后的括号内打“”；错误的在题后的括号内打“”.每小题 2 分，共 18 分）1任意数域 F
33、 可以看成是它自身上的向量空间.()2欧氏空间的两个子空间的并还是子空间 ()3.一个向量组存在两个极大无关组，它们所含向量的个数不相同.()4两个向量空间之间的同构映射的逆映射1还是同构映射.()5若数域 F 上的两个n阶矩阵 A、B 相似，则 A、B 合同.()6任何一个n阶实对称矩阵 A都相似且合同于一个实对角矩阵.()7两个复二次型等价的充要条件是它们有相同的秩.()8向量空间 V 的可逆线性变换的核)(Ker是空集.()9两个n阶正交矩阵 A、B 的和还是正交矩阵.()二得分阅卷教师二单项选择题（在每小题的四个备选答案中，选出一个正确的答案，并将其号码填在题目的括号内.每小题 2 分
34、，共 10分）1.下列命题正确的是 ().A.线性变换保持向量长度不变；B.对称变换保持向量的内积不变；C.正交变换保持向量夹角不变；D.线性变换保持向量的线性无关性.2两个 n 元实二次型等价的充要条件是().A它们的秩相等；B它们的惯性指标相等；C 它们的符号差相同；D它们有相同的秩和符号差.3数域 F 上所有对称矩阵的全体关于矩阵的加法及数乘所成的向量空间的维数是().A.2)1(nn；B.1n；C.2n；D.2)1(nn.装订线文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6
35、F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10
36、C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C
37、6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6
38、Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L
39、10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B
40、8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1
41、E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F97 4.向量空间2R 中的下列变换，只有()不是2R 的线性变换.A.),(),(xyyx；B.),(),(yxyx；C.)0,0(),(yx；D.),(),(yxyxyx5设 U 是一个n阶酉矩阵，则 ().A.U 的行列式等于 1；B.U 的特征根的模为 1；C.U 的行列式的模等于 1或1；D.U 的特征根为 1或1.三得 分阅卷教师三填空题（每小题2 分，共 10 分，把答案填在题中横线上）1.3 元实二次型32
42、31232221321222),(xmxxxxxxxxxf是正定的，则m取值范围为 .2.设 A是 n 阶实对称矩阵,则 A为正定的充要条件是.3.向量空间3R 中,向量(1,2,3)在基(1,1,1),(0,1,1),(0,0，1)下的坐标为.4.设是数域 F 上向量空间 V 的线性变换，W 是V 的子空间，则 W是的不变子空间的充分必要条件是5.在欧氏空间 V 中，V,baC,柯西-施瓦茨不等式成立，且等式成立：,2的充要条件是四得分阅卷教师五计算题（每小题 14 分，共 42 分）1求齐次线性方程组033030432143214321xxxxxxxxxxxx的解空间的一个基，再进一步实施
43、正交化，求出规范正交基文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档
44、编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7
45、H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R
46、5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9
47、文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3
48、K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E
49、3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F98 2设110310002A,求 A的特征根及对应的特征向量.问 A是否可以对角化？若可以，则求一可逆矩阵T，使ATT1为对角形.文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7
50、H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R5 ZO7S1E6Q6F9文档编码:CF1L10C3K7H2 HA1B8C6E3R