1、電視大學(xué) “開放本科” 工程數(shù)學(xué)(本) 試題一、單項(xiàng)選擇題(每小題3分，共15分) 1設(shè)a，b為n階矩陣，則下列等式成立的是( ) 3下列命題中不正確的是( ) a. a與a有相同的特征多項(xiàng)式 b若是a的特征值，則(入ia)xo的非零解向量必是a對(duì)應(yīng)于的特征向量 c. 若0是a的一個(gè)特征值，則axo必有非零解 da的特征向量的線性組合仍為a的特征向量 4若事件a與b互斥，則下列等式中正確的是( ) 二、填空題(每小題3分，共15分) 7設(shè)4元線性方程組ax月有解且r(a)1，那么ax月的相應(yīng)齊次方程組的基礎(chǔ)解 系含有個(gè)解向量 8設(shè)a，月互不相容，且p(a)0，則戶(ba)= 9設(shè)隨機(jī)變量xb(

2、n，p)，則正(x)三、計(jì)算題(每小題16分，共64分)12求下列線性方程組的通解 13設(shè)隨機(jī)變量xn(3，4)求：(1)p(1x7)；(2)使p(xa)09成立的常數(shù)a (已知 (10)=08413， (128)09， (20)09773) 14從正態(tài)總體n(，4)中抽取容量為625的樣本，計(jì)算樣本均值得25，求的置信度為99的置信區(qū)間(已知u0.9952576) 四、證明題(本題6分) 15設(shè)n階矩陣a滿足(ai)(a+i)o，則a為可逆矩陣試卷代號(hào)：1080 中央廣播電視大學(xué)20102011學(xué)年度第一學(xué)期“開放本科”期末考試(半開卷)工程數(shù)學(xué)(本) 試題答案及評(píng)分標(biāo)準(zhǔn)(供參考) 2011

3、年1月 一、單項(xiàng)選擇題(每小題3分，共15分) 1a 2b 3d 4a 5c 二、填空題(每小題3分，共15分) 61，-1，2，-2 7 3 8 0 9 np 三、計(jì)算題(每小題16分，共64分) 11解：由矩陣乘法和轉(zhuǎn)置運(yùn)算得利用初等行變換得12解：利用初等行變換，將方程組的增廣矩陣化成行簡化階梯形矩陣，即方程組的導(dǎo)出組的一般解為： 令x2l，x40，得導(dǎo)出組的解向量x2(2，1，0，0)； 令x2o，x41，得導(dǎo)出組的解向量x2(1，0，一1，1) 13分 所以方程組的通解為： 其中k1，k2是任意實(shí)數(shù) 16分四、證明題(本題6分) 15證明：因?yàn)?ai)(a+i)a2一io，即a2i

4、所以，a為可逆矩陣6分winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into th

5、e encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league inter

6、national federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all

7、blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will atte

8、nd citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against csk

9、afor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added:

10、 we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no preci

11、pitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cr

12、uising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out

13、onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they co

14、nceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests

15、 - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis are a l