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1、全國(guó)2008年10月高等教育自學(xué)考試線性代數(shù)(經(jīng)管類)試題答案課程代碼:04184一、單項(xiàng)選擇題(本大題共10小題,每小題2分,共20分)1設(shè)a為3階方陣,且,則(a)a-9b-3c-1d9,2設(shè)a、b為n階方陣,滿足,則必有(d)abcd3已知矩陣a=,b=,則(a)abcd=4設(shè)a是2階可逆矩陣,則下列矩陣中與a等價(jià)的矩陣是(d)abcd5設(shè)向量,下列命題中正確的是(b)a若線性相關(guān),則必有線性相關(guān)b若線性無關(guān),則必有線性無關(guān)c若線性相關(guān),則必有線性無關(guān)d若線性無關(guān),則必有線性相關(guān)6已知是齊次線性方程組ax=0的兩個(gè)解,則矩陣a可為(a)abcd,7設(shè)m×n矩陣a的秩r(a)=n

2、-3(n>3),是齊次線性方程組ax=0的三個(gè)線性無關(guān)的解向量,則方程組ax=0的基礎(chǔ)解系為(d)abcd其中只有線性無關(guān)8已知矩陣a與對(duì)角矩陣d=相似,則(c)aabdced存在,使,9設(shè)矩陣a=,則a的特征值為(d)a1,1,0b-1,1,1c1,1,1d1,-1,-110設(shè)a為n()階矩陣,且,則必有(c)aa的行列式等于1ba的逆矩陣等于eca的秩等于nda的特征值均為1,a的秩等于n二、填空題(本大題共10小題,每小題2分,共20分)11已知行列式,則數(shù)a =_3_,12設(shè)方程組有非零解,則數(shù)k = _4_,13設(shè)矩陣a=,b=,則=14已知向量組的秩為2,則數(shù)t=_3_,秩為

3、2,則15設(shè)向量,則的長(zhǎng)度為_5/2_16設(shè)向量組,與向量組等價(jià),則向量組的秩為_2_,秩為217已知3階矩陣a的3個(gè)特征值為,則_36_18設(shè)3階實(shí)對(duì)稱矩陣a的特征值為,則r(a)= _2_a相似于,r(a)=219矩陣a=對(duì)應(yīng)的二次型f =20設(shè)矩陣a=,則二次型的規(guī)范形是,其中,三、計(jì)算題(本大題共6小題,每小題9分,共54分)21計(jì)算行列式d=的值解:22已知a=,b=,c=,矩陣x滿足axb=c,求解x解:,;,=23求向量在基,下的坐標(biāo),并將用此基線性表示解:設(shè),即,得,在基下的坐標(biāo)是,24設(shè)向量組線性無關(guān),令,試確定向量組的線性相關(guān)性解:設(shè),即,由線性無關(guān),得,有非零解,線性相關(guān)

4、25已知線性方程組,(1)討論為何值時(shí),方程組無解、有惟一解、有無窮多個(gè)解(2)在方程組有無窮多個(gè)解時(shí),求出方程組的通解(用一個(gè)特解和導(dǎo)出組的基礎(chǔ)解系表示)解:(1)時(shí)無解,且時(shí)惟一解,時(shí)有無窮多個(gè)解(2)時(shí),通解為26已知矩陣a=,求正交矩陣p和對(duì)角矩陣,使解:,特征值,對(duì)于,解齊次線性方程組:,基礎(chǔ)解系為,正交化:令,單位化:令,;對(duì)于,解齊次線性方程組:,基礎(chǔ)解系為,單位化:令令,則p是正交矩陣,使四、證明題(本題6分)27設(shè)為非齊次線性方程組ax=b的一個(gè)解,是其導(dǎo)出組ax=0的一個(gè)基礎(chǔ)解系證明線性無關(guān)證:設(shè),則,由,得-(1)從而,由線性無關(guān),得-(2)由(1)(2)可知線性無關(guān)th

5、at construction 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 co

6、ncealed work-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

7、 follow construction progress at any time finishing self acceptance, signature acceptance after the representatives of the party were invited. requirements: (1) covert acceptance is thea the company's situation, familiar with the period schedule master plan, construction with water, power supply

8、, vertical transportation, 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 qualit

9、y standards, safety 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 to

10、ols and appliances. (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

11、(early works with 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 de

12、gree of precision 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 overal

13、l effect. 2. material 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, siz

14、e error in 0.5mm stone. 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 a

15、ppropriate authority 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 tu

16、rned received pieces 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 s

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