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1、专业好文档电视大学 “开放本科” 工程数学(本) 试题一、单项选择题(每小题3分，共15分) 1设A，B为n阶矩阵，则下列等式成立的是( ) 3下列命题中不正确的是( ) A. A与A有相同的特征多项式 B若是A的特征值，则(入IA)XO的非零解向量必是A对应于的特征向量 C. 若0是A的一个特征值，则AXO必有非零解 DA的特征向量的线性组合仍为A的特征向量 4若事件A与B互斥，则下列等式中正确的是( ) 二、填空题(每小题3分，共15分) 7设4元线性方程组AX月有解且r(A)1，那么AX月的相应齐次方程组的基础解 系含有个解向量 8设A，月互不相容，且P(A)0，则户(BA)= 9设随机
2、变量XB(n，p)，则正(X)三、计算题(每小题16分，共64分)12求下列线性方程组的通解 13设随机变量XN(3，4)求：(1)P(1X7)；(2)使P(Xa)09成立的常数a (已知 (10)=08413， (128)09， (20)09773) 14从正态总体N(，4)中抽取容量为625的样本，计算样本均值得25，求的置信度为99的置信区间(已知u0.9952576) 四、证明题(本题6分) 15设n阶矩阵A满足(AI)(A+I)O，则A为可逆矩阵试卷代号：1080 中央广播电视大学20102011学年度第一学期“开放本科”期末考试(半开卷)工程数学(本) 试题答案及评分标准(供参考)
3、 2011年1月 一、单项选择题(每小题3分，共15分) 1A 2B 3D 4A 5C 二、填空题(每小题3分，共15分) 61，-1，2，-2 7 3 8 0 9 Np 三、计算题(每小题16分，共64分) 11解：由矩阵乘法和转置运算得利用初等行变换得12解：利用初等行变换，将方程组的增广矩阵化成行简化阶梯形矩阵，即方程组的导出组的一般解为： 令x2l，x40，得导出组的解向量X2(2，1，0，0)； 令x2o，x41，得导出组的解向量X2(1，0，一1，1) 13分 所以方程组的通解为： 其中k1，k2是任意实数 16分四、证明题(本题6分) 15证明：因为(AI)(A+I)A2一IO，
4、即A2I 所以，A为可逆矩阵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 in
5、to the 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
6、International 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
7、 All 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
8、 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 agains
9、t 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 a
10、dded: 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
11、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 t
12、he 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
13、 out 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 th
14、ey conceded 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 con
15、tests - 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
16、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 lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.