《电大工程数学作业（1~3）形成性考核册答案.doc》由会员分享，可在线阅读，更多相关《电大工程数学作业（1~3）形成性考核册答案.doc（13页珍藏版）》请在三一办公上搜索。
1、电大工程数学作业（13）形成性考核册答案工程数学作业（一）答案（满分100分）第2章 矩阵（一） 单项选择题（每小题2分，共20分） 设，则（D） A. 4 B. 4 C. 6 D. 6 若，则（A） A. B. 1 C. D. 1 乘积矩阵中元素（C） A. 1 B. 7 C. 10 D. 8 设均为阶可逆矩阵，则下列运算关系正确的是（B） A. B. C. D. 设均为阶方阵，且，则下列等式正确的是（D） A. B. C. D. 下列结论正确的是（A） A. 若是正交矩阵，则也是正交矩阵 B. 若均为阶对称矩阵，则也是对称矩阵 C. 若均为阶非零矩阵，则也是非零矩阵 D. 若均为阶非零矩阵
2、，则 矩阵的伴随矩阵为（C） A. B. C. D. 方阵可逆的充分必要条件是（B） A. B. C. D. 设均为阶可逆矩阵，则（D） A. B. C. D. 设均为阶可逆矩阵，则下列等式成立的是（A） A. B. C. D. （二）填空题（每小题2分，共20分） 7 是关于的一个一次多项式，则该多项式一次项的系数是 2 若为矩阵，为矩阵，切乘积有意义，则为 54 矩阵 二阶矩阵 设，则 设均为3阶矩阵，且，则 72 设均为3阶矩阵，且，则 3 若为正交矩阵，则 0 矩阵的秩为 2 设是两个可逆矩阵，则（三）解答题（每小题8分，共48分） 设，求；答案： 设，求解： 已知，求满足方程中的解：
3、 写出4阶行列式中元素的代数余子式，并求其值答案： 用初等行变换求下列矩阵的逆矩阵： ； ； 解：（1）（2）(过程略) (3) 求矩阵的秩解： （四）证明题（每小题4分，共12分） 对任意方阵，试证是对称矩阵证明： 是对称矩阵 若是阶方阵，且，试证或 证明： 是阶方阵，且或 若是正交矩阵，试证也是正交矩阵证明： 是正交矩阵 即是正交矩阵工程数学作业（第二次）(满分100分)第3章 线性方程组（一）单项选择题(每小题2分，共16分) 用消元法得的解为（C） A. B. C. D. 线性方程组（B） A. 有无穷多解 B. 有唯一解 C. 无解 D. 只有零解 向量组的秩为（A） A. 3 B.
4、 2 C. 4 D. 5 设向量组为，则（B）是极大无关组 A. B. C. D. 与分别代表一个线性方程组的系数矩阵和增广矩阵，若这个方程组无解，则（D） A. 秩秩 B. 秩秩 C. 秩秩 D. 秩秩 若某个线性方程组相应的齐次线性方程组只有零解，则该线性方程组（A） A. 可能无解 B. 有唯一解 C. 有无穷多解 D. 无解 以下结论正确的是（D） A. 方程个数小于未知量个数的线性方程组一定有解 B. 方程个数等于未知量个数的线性方程组一定有唯一解 C. 方程个数大于未知量个数的线性方程组一定有无穷多解 D. 齐次线性方程组一定有解 若向量组线性相关，则向量组内（A）可被该向量组内其
5、余向量线性表出 A. 至少有一个向量 B. 没有一个向量 C. 至多有一个向量 D. 任何一个向量9设A，为阶矩阵，既是又是的特征值，既是又是的属于的特征向量，则结论（）成立是AB的特征值 是A+B的特征值是AB的特征值 是A+B的属于的特征向量10设，为阶矩阵，若等式（）成立，则称和相似（二）填空题(每小题2分，共16分) 当 时，齐次线性方程组有非零解 向量组线性 相关 向量组的秩是 设齐次线性方程组的系数行列式，则这个方程组有 无穷多 解，且系数列向量是线性 相关 的 向量组的极大线性无关组是 向量组的秩与矩阵的秩 相同 设线性方程组中有5个未知量，且秩，则其基础解系中线性无关的解向量有
6、 个 设线性方程组有解，是它的一个特解，且的基础解系为，则的通解为 9若是的特征值，则是方程的根10若矩阵满足，则称为正交矩阵（三）解答题(第1小题9分，其余每小题11分) 1用消元法解线性方程组解：方程组解为设有线性方程组为何值时，方程组有唯一解?或有无穷多解?解：当且时，方程组有唯一解当时，方程组有无穷多解 判断向量能否由向量组线性表出，若能，写出一种表出方式其中 解：向量能否由向量组线性表出，当且仅当方程组有解这里方程组无解不能由向量线性表出 计算下列向量组的秩，并且（1）判断该向量组是否线性相关 解：该向量组线性相关 求齐次线性方程组的一个基础解系解：方程组的一般解为令，得基础解系 求
7、下列线性方程组的全部解解：方程组一般解为令，这里，为任意常数，得方程组通解试证：任一维向量都可由向量组，线性表示，且表示方式唯一，写出这种表示方式证明：任一维向量可唯一表示为试证：线性方程组有解时，它有唯一解的充分必要条件是：相应的齐次线性方程组只有零解证明：设为含个未知量的线性方程组该方程组有解，即从而有唯一解当且仅当而相应齐次线性方程组只有零解的充分必要条件是有唯一解的充分必要条件是：相应的齐次线性方程组只有零解9设是可逆矩阵的特征值，且，试证：是矩阵的特征值证明：是可逆矩阵的特征值存在向量，使即是矩阵的特征值10用配方法将二次型化为标准型解：令，即则将二次型化为标准型工程数学作业（第三次
8、）(满分100分)第4章 随机事件与概率（一）单项选择题 为两个事件，则（B）成立 A. B. C. D. 如果（C）成立，则事件与互为对立事件 A. B. C. 且 D. 与互为对立事件 10张奖券中含有3张中奖的奖券，每人购买1张，则前3个购买者中恰有1人中奖的概率为（D） A. B. C. D. 4. 对于事件，命题（C）是正确的 A. 如果互不相容，则互不相容 B. 如果，则 C. 如果对立，则对立 D. 如果相容，则相容某随机试验的成功率为,则在3次重复试验中至少失败1次的概率为（D） A. B. C. D. 6.设随机变量，且，则参数与分别是（A） A. 6, 0.8 B. 8,
9、0.6 C. 12, 0.4 D. 14, 0.27.设为连续型随机变量的密度函数，则对任意的，（A） A. B. C. D. 8.在下列函数中可以作为分布密度函数的是（B） A. B. C. D. 9.设连续型随机变量的密度函数为，分布函数为，则对任意的区间，则（D） A. B. C. D. 10.设为随机变量，当（C）时，有 A. B. C. D. （二）填空题从数字1,2,3,4,5中任取3个，组成没有重复数字的三位数，则这个三位数是偶数的概率为2.已知，则当事件互不相容时， 0.8 ， 0.3 3.为两个事件，且，则4. 已知，则5. 若事件相互独立，且，则6. 已知，则当事件相互独立
10、时， 0.65 ， 0.3 7.设随机变量，则的分布函数8.若，则 6 9.若，则10.称为二维随机变量的 协方差 （三）解答题1.设为三个事件，试用的运算分别表示下列事件： 中至少有一个发生； 中只有一个发生； 中至多有一个发生； 中至少有两个发生； 中不多于两个发生； 中只有发生解:(1) (2) (3) (4) (5) (6)2. 袋中有3个红球，2个白球，现从中随机抽取2个球，求下列事件的概率： 2球恰好同色； 2球中至少有1红球解:设=“2球恰好同色”，=“2球中至少有1红球” 3. 加工某种零件需要两道工序，第一道工序的次品率是2%，如果第一道工序出次品则此零件为次品；如果第一道工
11、序出正品，则由第二道工序加工，第二道工序的次品率是3%，求加工出来的零件是正品的概率解：设“第i道工序出正品”（i=1,2）4. 市场供应的热水瓶中，甲厂产品占50%，乙厂产品占30%，丙厂产品占20%，甲、乙、丙厂产品的合格率分别为90%,85%,80%，求买到一个热水瓶是合格品的概率解：设 5. 某射手连续向一目标射击，直到命中为止已知他每发命中的概率是，求所需设计次数的概率分布解：故X的概率分布是6.设随机变量的概率分布为试求解：7.设随机变量具有概率密度试求解：8. 设，求解：9. 设，计算；解：10.设是独立同分布的随机变量，已知，设，求解： 以上内容可能会有错误，欢迎指出请您删除一
12、下内容，O(_)O谢谢！【Chinas 10 must-see animations】The Chinese animation industry has seen considerable growth in the last several years. It went through a golden age in the late 1970s and 1980s when successively brilliant animation work was produced. Here are 10 must-see classics from Chinas animation outp
13、ouring that are not to be missed. Lets recall these colorful images that brought the country great joy. Calabash Brothers Calabash Brothers (Chinese: 葫芦娃) is a Chinese animation TV series produced byShanghaiAnimationFilmStudio. In the 1980s the series was one of the most popular animations in China.
14、 It was released at a point when the Chinese animation industry was in a relatively downed state compared to the rest of the international community. Still, the series was translated into 7 different languages. The episodes were produced with a vast amount of paper-cut animations. Black Cat Detectiv
15、e Black Cat Detective (Chinese: 黑猫警长) is a Chinese animation television series produced by the Shanghai Animation Film Studio. It is sometimes known as Mr. Black. The series was originally aired from 1984 to 1987. In June 2006, a rebroadcasting of the original series was announced. Critics bemoan th
16、e series violence, and lack of suitability for childrens education. Proponents of the show claim that it is merely for entertainment. Effendi Effendi, meaning sir andteacher in Turkish, is the respectful name for people who own wisdom and knowledge. The heros real name was Nasreddin. He was wise and
17、 witty and, more importantly, he had the courage to resist the exploitation of noblemen. He was also full of compassion and tried his best to help poor people. Adventure of Shuke and Beita【舒克与贝塔】 Adventure of Shuke and Beita (Chinese: 舒克和贝塔) is a classic animation by Zheng Yuanjie, who is known as K
18、ing of Fairy Tales in China. Shuke and Beita are two mice who dont want to steal food like other mice. Shuke became a pilot and Beita became a tank driver, and the pair met accidentally and became good friends. Then they befriended a boy named Pipilu. With the help of PiPilu, they co-founded an airl
19、ine named Shuke Beita Airlines to help other animals. Although there are only 13 episodes in this series, the content is very compact and attractive. The animation shows the preciousness of friendship and how people should be brave when facing difficulties. Even adults recalling this animation today
20、 can still feel touched by some scenes. Secrets of the Heavenly Book Secrets of the Heavenly Book, (Chinese: 天书奇谈)also referred to as Legend of the Sealed Book or Tales about the Heavenly Book, was released in 1983. The film was produced with rigorous dubbing and fluid combination of music and vivid
21、 animations. The story is based on the classic literature Ping Yao Zhuan, meaning The Suppression of the Demons by Feng Menglong. Yuangong, the deacon, opened the shrine and exposed the holy book to the human world. He carved the books contents on the stone wall of a white cloud cave in the mountain
22、s. He was then punished with guarding the book for life by the jade emperor for breaking heavens law. In order to pass this holy book to human beings, he would have to get by the antagonist fox. The whole animation is characterized by charming Chinesepainting, including pavilions, ancient architectu
23、re, rippling streams and crowded markets, which fully demonstrate the unique beauty of Chinas natural scenery. Pleasant Goat and Big Big Wolf【喜洋洋与灰太狼】 Pleasant Goat and Big Big Wolf (Chinese:喜羊羊与灰太狼) is a Chinese animated television series. The show is about a group of goats living on the Green Past
24、ure, and the story revolves around a clumsy wolf who wants to eat them. It is a popular domestic animation series and has been adapted intomovies. Nezha Conquers the Dragon King（Chinese: 哪吒闹海）is an outstanding animation issued by the Ministry of Culture in 1979 and is based on an episode from the Ch
25、inese mythological novel Fengshen Yanyi. A mother gave birth to a ball of flesh shaped like a lotus bud. The father, Li Jing, chopped open the ball, and beautiful boy, Nezha, sprung out. One day, when Nezha was seven years old, he went to the nearby seashore for a swim and killed the third son of th
26、e Dragon King who was persecuting local residents. The story primarily revolves around the Dragon Kings feud with Nezha over his sons death. Through bravery and wit, Nezha finally broke into the underwater palace and successfully defeated him. The film shows various kinds of attractive sceneries and
27、 the traditional culture of China, such as spectacular mountains, elegant sea waves and exquisite ancient Chinese clothes. It has received a variety of awards. Havoc in Heaven The story of Havoc in Heaven（Chinese: 大闹天宫）is based on the earliest chapters of the classic storyJourney to the West. The ma
28、in character is Sun Wukong, aka the Monkey King, who rebels against the Jade Emperor of heaven. The stylized animation and drums and percussion accompaniment used in this film are heavily influenced byBeijingOpera traditions. The name of the movie became a colloquialism in the Chinese language to de
29、scribe someone making a mess. Regardless that it was an animated film, it still became one of the most influential films in all of Asia. Countless cartoon adaptations that followed have reused the same classic story Journey to the West, yet many consider this 1964 iteration to be the most original,
30、fitting and memorable, The Golden Monkey Defeats a Demon【金猴降妖】 The Golden Monkey Defeats a Demon (Chinese: 金猴降妖), also referred as The Monkey King Conquers the Demon, is adapted from chapters of the Chinese classics Journey to the West, or Monkey in the Western world. The five-episode animation seri
31、es tells the story of Monkey King Sun Wukong, who followed Monk Xuan Zangs trip to the West to take the Buddhistic sutra. They met a white bone evil, and the evil transformed human appearances three times to seduce the monk. Twice Monkey King recognized it and brought it down. The monk was unable to
32、 recognize the monster and expelled Sun Wukong. Xuan Zang was then captured by the monster. Fortunately Bajie, another apprentice of Xuan Zang, escaped and persuaded the Monkey King to come rescue the monk. Finally, Sun kills the evil and saves Xuan Zang. The outstanding animation has received a var
33、iety of awards, including the 6th Hundred Flowers Festival Award and the Chicago International Childrens Film Festival Award in 1989. McDull【麦兜】 McDull is a cartoon pig character that was created inHong Kongby Alice Mak and Brian Tse. Although McDull made his first appearances as a supporting charac
34、ter in the McMug comics, McDull has since become a central character in his own right, attracting a huge following in Hong Kong. The first McDull movie McMug Story My Life as McDull documented his life and the relationship between him and his mother.The McMug Story My Life as McDull is also being translated into French and shown in France. In this version, Mak Bing is the mother of McDull, not his father. 13
