2008年10月线性代数(经管类)试题及答案

1、全国2008年10月高等教育自学考试线性代数（经管类）试题答案课程代码：04184一、单项选择题（本大题共10小题，每小题2分，共20分）1设A为3阶方阵，且，则（A）A-9B-3C-1D9，2设A、B为n阶方阵，满足，则必有（D）ABCD3已知矩阵A=，B=，则（A）ABCD=4设A是2阶可逆矩阵，则下列矩阵中与A等价的矩阵是（D）ABCD5设向量，下列命题中正确的是（B）A若线性相关，则必有线性相关B若线性无关，则必有线性无关C若线性相关，则必有线性无关D若线性无关，则必有线性相关6已知是齐次线性方程组Ax=0的两个解，则矩阵A可为（A）ABCD，7设mn矩阵A的秩r(A)=n-3（n3）

2、，是齐次线性方程组Ax=0的三个线性无关的解向量，则方程组Ax=0的基础解系为（D）ABCD其中只有线性无关8已知矩阵A与对角矩阵D=相似，则（C）AABDCED存在，使，9设矩阵A=，则A的特征值为（D）A1，1，0B-1，1，1C1，1，1D1，-1，-110设A为n（）阶矩阵，且，则必有（C）AA的行列式等于1BA的逆矩阵等于ECA的秩等于nDA的特征值均为1，A的秩等于n二、填空题（本大题共10小题，每小题2分，共20分）11已知行列式，则数a =_3_，12设方程组有非零解，则数k = _4_，13设矩阵A=，B=，则=14已知向量组的秩为2，则数t=_3_，秩为2，则15设向量，则

3、的长度为_5/2_16设向量组，与向量组等价，则向量组的秩为_2_，秩为217已知3阶矩阵A的3个特征值为，则_36_18设3阶实对称矩阵A的特征值为，则r(A)= _2_A相似于，r(A)=219矩阵A=对应的二次型f =20设矩阵A=，则二次型的规范形是，其中，三、计算题（本大题共6小题，每小题9分，共54分）21计算行列式D=的值解：22已知A=，B=，C=，矩阵X满足AXB=C，求解X解：，；，=23求向量在基，下的坐标，并将用此基线性表示解：设，即，得，在基下的坐标是，24设向量组线性无关，令，试确定向量组的线性相关性解：设，即，由线性无关，得，有非零解，线性相关25已知线性方程组，

4、（1）讨论为何值时，方程组无解、有惟一解、有无穷多个解（2）在方程组有无穷多个解时，求出方程组的通解（用一个特解和导出组的基础解系表示）解：（1）时无解，且时惟一解，时有无穷多个解（2）时，通解为26已知矩阵A=，求正交矩阵P和对角矩阵，使解：，特征值，对于，解齐次线性方程组：，基础解系为，正交化：令，单位化：令，；对于，解齐次线性方程组：，基础解系为，单位化：令令，则P是正交矩阵，使四、证明题（本题6分）27设为非齐次线性方程组Ax=b的一个解，是其导出组Ax=0的一个基础解系证明线性无关证：设，则，由，得-（1）从而，由线性无关，得-（2）由（1）（2）可知线性无关that constru

5、ction site clean, consciously maintain sanitation. (4) ensure the safety of materials and semi-finished products. 8. quality assessment, data compilation: buried, belongs to the concealed works construction, therefore its quality inspection must be carried out according to acceptance of concealed wo

6、rk-related. Mainly in the following aspects: (1) acceptance of positioning is accurate. (2) is fixed securely. (3) tightening compliance requirements. (4) have an impact on other projects. (5) the material used is eligible. (6) complete information has been collected. Documentation: should follow co

7、nstruction progress at any time finishing self acceptance, signature acceptance after the representatives of the party were invited. Requirements: (1) covert acceptance is thea the companys situation, familiar with the period schedule master plan, construction with water, power supply, vertical tran

8、sportation, gondola of external scaffolding or construction. (2) technical data preparation: first drawings to prepare the drawings to be fully familiar with, and does not have difficult places to ask out clearly understood, you also need to prepare acceptance of the Atlas, the quality standards, sa

9、fety index, all the forms used and the acceptance required for the works, and more. (3) tools, implements preparation: supply planning against the required tools, appliances, specific to the type, quantity, supply time, also plans to supply, warehouse, and other departments, common tools and applian

10、ces. (4) materials: according to the drawings and engineering, detailed material supply meter . (2) preparations into people, and clear accountability to specific persons. (3) implementation of collaboration and cooperation with construction companies. 2.15 embedded part installation (early works wi

11、th civil engineering completed) 1. Note: buried is one of the curtain wall with main structure connecting structure, embedded quality directly affects the production, installation of curtain wall and the main structure of the connections. Its installation has a direct impact on the degree of precisi

12、on of curtain wall construction accuracy and surface quality is good or bad. So the first job as a curtain wall installation, buried both for its manufacture and installation are directly affects the entire curtain wall construction, installation, and an important factor in the overall effect. 2. ma

13、terial specifications: the embedded parts. 3. basic operation: (1) familiar with the drawings: installation personnel after receivingtypeset by the owners consent before they can purchase and order under the program, each stone must use the same background, the same pattern, size error in 0.5mm ston

14、e. Air infiltration properties, stone curtain wall wind pressure rainwater leakage in distortion performance, performance and energy-saving performance in front of the construction should be in accordance with the construction plan of the specification and the file size in the appropriate authority

15、inspection departments qualified testing. Stone used steel keel, installation job main including following steps: 2.1 construction Qian prepared 2.2 pre buried pieces processing 2.3 measurement and the measurement results figure draws 2.4 vertical box positioning put line 2.5 turned received pieces

16、installation 2.6 vertical box installation 2.7 vertical box correction and acceptance 2.8 layer high and the cross box measurement positioning and put line 2.9 cross box installation 2.10 installation 2.11 stone plate installation 2.12 sealed rubber injection 2.13 clean ending 2.14 construction Qian prepared 1. Description Project Manager required for the duration of the project sc