2017年電大《工程數(shù)學》廣播電視大學歷年期末試題及答案小抄參考.doc

專業(yè)好文檔試卷代號：1080中央廣播電視大學20112012學年度第一學期“開放本科”期末考試（半開卷）工程數(shù)學(本) 試題2012年1月一、單項選擇題(每小題3分，共15分)1 設，為三階可逆矩陣，且，則下列（ ）成立A B C D 2 設是n階方陣，當條件（ ）成立時，n元線性方程組有惟一解AE3設矩陣的特征值為0，2，則的特征值為（ ）。A0，2 B0，6C0，0 D2，64若隨機變量，則隨機變量 ( )5 對正態(tài)總體方差的檢驗用( )二、填空題(每小題3分，共15分)6 設均為二階可逆矩陣，則 8 設 A， B 為兩個事件，若,則稱A與B9若隨機變量，則 10若都是的無偏估計，且滿足_，則稱比更有效。三、計算題(每小題16分，共64分)11 設矩陣，那么可逆嗎？若可逆，求逆矩陣12在線性方程組中取何值時，此方程組有解。在有解的情況下，求出通解。13. 設隨機變量,求和。 (已知，)14. 某切割機在正常工作時，切割的每段金屬棒長服從正態(tài)分布，且其平均長度為10.5cm，標準差為0.15cm。從一批產(chǎn)品中隨機地抽取4段進行測量，測得的結果如下：（單位：cm）10.4, 10.6, 10.1, 10.4問：該機工作是否正常（）？四、證明題（本題6分）15. 設n階矩陣A滿足,試證A為對稱矩陣。參考解答一、單項選擇題(每小題3分，共15分) 1、B 2、A 3、B 4、D 5、C 二、填空題(每小題3分，共15分)三、計算題(每小題16分，共64分)試卷代號：1080中央廣播電視大學20102011學年度第二學期“開放本科”期末考試（半開卷）工程數(shù)學(本) 試題2011年7月一、單項選擇題(每小題3分，共15分)1 設，都是n階方陣，則等式（ ）成立A B C D2 已知2維向量組則至多是 AS（ ）。AE A、1 B、2 C、3 D、43線性方程組解的情況是（ ）。A無解 B有惟一非零解C只有零解 D有無窮多解4對任意兩個事件 A，B，等式( )成立A B C D5 設是來自正態(tài)總體的樣本，則 ( ) 是統(tǒng)計量A B C D二、填空題(每小題3分，共15分)1 設A,B是3階方陣，其中則2 設A為n階方陣，若存在數(shù)和非零n維向量，使得，則稱為A的_。3 若，則 4設隨機變量，若,則 5若參數(shù)的兩個無偏估計量和滿足，則稱比更_三、計算題(每小題16分，共64分)1 設矩陣，,求2設齊次線性方程組，為何值時，方程組有非零解？在有非零解時求其通解。3. 設,求(1)；（2）。4. 某鋼廠生產(chǎn)了一批管材，每根標準直徑100mm，今對這批管材進行檢驗，隨機取出9根測得直徑的平均值為99.9mm，樣本標準差s=0.47，已知管材直徑服從正態(tài)分布，問這批管材的質(zhì)量是否合格？（檢驗顯著性水平）四、證明題（本題6分）設A是可逆的對稱矩陣，試證：也是對稱矩陣。參考答案一、單項選擇題(每小題3分，共15分) 1、C 2、B 3、A 4、D 5、B 二、填空題(每小題3分，共15分)1122特征值30.343 5. 有效三、計算題(每小題16分，共64分)四、證明題（本題6分）試卷代號：1080中央廣播電視大學20102011學年度第一學期“開放本科”期末考試（半開卷）工程數(shù)學(本) 試題2011年1月一、單項選擇題(每小題3分，共15分)1 設，都是n階方陣，則下列等式成立的是（ ）A B C D 2 方程組相容的充分必要條件是 AS（ ），其中AE3下列命題中不正確的是（ ）。A有相同的特征多項式 B若是 A 的特征值，則的非零解向量必是 A 對應于的特征向量C若是A的一個特征值，則AX=O 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( )5 設是來自正態(tài)總體的樣本，則檢驗假設采用統(tǒng)計量 ( )二、填空題(每小題3分，共15分)6 設，則的根是7設4 元錢性方程提 AX=B 有解且，那么的相應齊次方程程的基礎解系含有_個解向量。8 設 A， B 互不相容，且 P(A)O ，則 9設隨機變量，則 10若樣本來自總體，且，則_三、計算題(每小題16分，共64分)11 設矩陣，求12求下列線性方程組的通解。13. 設隨機變量,試求(1)；（2）使成立的常數(shù)。 (已知，)14. 從正態(tài)總體中抽取容量為625的樣本，計算樣本均值得，求的置信區(qū)間度為，99%的置信區(qū)間。（已知）四、證明題（本題6分）15. 設n階矩陣A滿足,則A為可逆矩陣。參考解答一、單項選擇題(每小題3分，共15分) 1、A 2、B 3、D 4、A 5、C 二、填空題(每小題3分，共15分)11,-1,2.,-223304np 5.三、計算題(每小題16分，共64分)試卷代號：1080中央廣播電視大學20092010學年度第二學期“開放本科”期末考試（半開卷）工程數(shù)學(本) 試題2010年7月一、單項選擇題(每小題3分，共15分)1 設，B都是n階方陣，則下列命題正確的是（ ）A B C D 2 向量組的秩是 AS（ ）AEA1 B3C 2 D43 n元線性方程組，有解的充分必要條件是（ ）。A BA不是行滿秩矩陣C D4 袋中有3個紅球，2個白球，第一次取出一球后放回，第二次再取一球，則兩球都是紅球的概率是 ( )A B C D 5 設是來自正態(tài)總體的樣本，則 ( )是無偏估計A BC D二、填空題(每小題3分，共15分)1 設均為3階方陣，且2設為階方陣，若存在數(shù)和非零維向量，使得_，則稱為的特征值3設隨機變量，則4設為隨機變量，已知，此時 5設是未知參數(shù)的一個無偏估計量，則有_三、計算題(每小題16分，共64分)1 設矩陣，且有，求2求線性方程組的全部解。3. 設,試求（1）；（2）。 (已知，)4. 據(jù)資料分析，某廠生產(chǎn)的一批磚，其抗斷強度，今從這批磚中隨機地抽取了9塊，測得抗斷強度（單位：）的平均值為31.12，問這批磚的抗斷強度是否合格？四、證明題（本題6分） 設是n階對稱矩陣，試證：也是對稱矩陣。參考解答一、單項選擇題(每小題3分，共15分) 1、A 2、B 3、A 4、D 5、C 二、填空題(每小題3分，共15分)1-18230.3427 5.三、計算題(每小題16分，共64分)1解：利用初等行變換得2解：將方程組的增廣矩陣化為階梯形試卷代號：1080中央廣播電視大學20092010學年度第一學期“開放本科”期末考試（半開卷）工程數(shù)學(本) 試題2010年1月一、單項選擇題(每小題3分，共15分)1 設為對稱矩陣，則條件（ ）成立A B C D 2 AS（ ）AEA BC D3 若 ( )成立，則元方程組有唯一解。A BC D的行向量組線性無關4 若條件 ( )成立，則隨機事件互為對立事件A B C D 5 對來自正態(tài)總體的一組樣本，記，則下列各式中 ( )不是統(tǒng)計量ABCD二、填空題(每小題3分，共15分)6 設均為3階方陣，且7設為階方陣，若存在數(shù)和非零維向量，使得_，則稱為相應于特征值的特征向量8若，則9如果隨機變量的期望且，那么 10不含未知參數(shù)的樣本函數(shù)稱為_三、計算題(每小題16分，共32分)11 設矩陣，求12當取何值時，線性方程組有解，在有解的情況下求出此方程組的一般解四、計算分析題（每小題16分，共32分）13. 設,試求（1）；（2）。 (已知，)14. 某車間生產(chǎn)滾珠，已知滾珠直徑服從正態(tài)分布，今從一批產(chǎn)品里隨機取出9 個，測得直徑平均值為15.1 mm，若已知這批滾珠直徑的方差為，試找出滾珠直徑均值的置信度為0.95的置信區(qū)間五、證明題（本題6分）15. 設隨機事件相互獨立，試證：也相互獨立。參考解答一、單項選擇題(每小題3分，共15分) 1、B 2、D 3、A 4、C 5、C 二、填空題(每小題3分，共15分)68780.3920 10統(tǒng)計量三、計算題(每小題16分，共64分)11解：利用初等行變換得12解：將方程組的增廣矩陣化為階梯形四、計算分析題（每小題16分，共32分）If we dont do that it will go on and go on. We have to stop it; we need the courage to do it.His comments came hours after Fifa vice-president Jeffrey Webb - also in London for the FAs celebrations - said he wanted to meet Ivory Coast international Toure to discuss his complaint.CSKA general director Roman Babaev says the matter has been exaggerated by the Ivorian and the British media.Blatter, 77, said: It has been decided by the Fifa congress that it is a nonsense for racism to be dealt with with fines. You can always find money from somebody to pay them.It is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. It is all nonsense.We can do something better to fight racism and discrimination.This is one of the villains we have today in our game. But it is only with harsh sanctions that racism and discrimination can be washed out of football.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 attend 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 CSKAfor 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: 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 precipitation 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 cruising 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 onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. Like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to Earth. But this will not be enough to stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. His team hopes its not needed. Instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).In order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have a reserve parachute that will open automatically if he loses consciousness at mach speeds.Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there第 23 頁 共 23 頁