北京航空航天大学2014年矩阵论考博真题解析

回忆版。

某些题目的描述可能会有不完全之处，但基本正确。

总分50分。

一、选择题（每题1分）1.IPV4有_____位。

A.64B.32C.128D.162.两个交换机组成一个连接，那么它_____。

（选项中的*代表一个名词，忘了）A. 既是一个*，又是一个冲突域B. 是一个*，不是一个冲突域C. 不是一个*，但是一个冲突域D. 既不是一个*，也不是一个冲突域3.202.5.151.10是一个______类地址。

（可能IP地址有出入，不过是以202开头的一个IP）A. AB.BC.CD.D4.从内部IP转换为外部IP的技术称为_____协议。

A.ARPB.NATC.HDCPD.RARP5. 线路长1km 的CSMA/CD网络，传播速率为2*105km/s，数据传输速率是1Gbps，则最小帧长为_____。

6.UDP传输协议解决拥塞控制所采用的算法_______。

（题目描述较长，但是实际就是考UDP 的拥塞控制算法，选项记不住了，本人选的是指数回退算法）7.网络协议的三个要素是______。

A.……B.……C. 语法、语义、时序D.……8……（记不住）二、填空题（每空1分）1.一对一的传输是________，一对多的传输是_______，_____传输是将数据包发送给最近的主机。

2.路由器是OSI的________层。

3.OSI分为七层，其顺序依次是物理层，______，网络层，______，_____，______，应用层。

4.1Gbps的带宽，时延为5ms，TCP发送窗口的大小是65535字节，吞吐量是____，网络利用率为______。

三、简答题（每题6分）1.TCP和UDP在以下几个方面的区别：是否连接；是否可靠；适用场合；传输速度。

2.给出路由器路由表如下（表格内容就是目的地网络/子网掩码/下一站），求以下6个地址的下一站。

（表格和地址都记不清了，和课后习题一样，会算就行。

）3.TCP的拥塞控制机制是否适用于无线网络，说明原因。

《矩阵理论》考试大纲科目代码：2001
基本内容与要求：
一、矩阵的基本知识：
1.矩阵的运算
2.逆矩阵、分块矩阵、矩阵的秩
3.初等变换与初等矩阵
二、线性方程组
1.向量组的线性相关性
2.线性方程组有解的判定定理及解的结构
三、矩阵的相似变换与二次型
1.方阵的特征值与特征向量
2.矩阵的相似对角化
3.矩阵的若当标准形
4.二次型的标准形、规范形及唯一性
5.正定二次型与正定矩阵
四、线性空间
1.线性空间的定义和性质
2.维数、基与坐标
3.线性子空间
4.欧氏空间
五、线性变换
1.线性变换的概念和基本性质
2.线性变换的矩阵
3.线性变换的特征值与特征向量
六、矩阵的分解
1.QR分解
2.正规矩阵及Schur分解
3.满秩分解
4.奇异值分解。

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2014年北京航空航天大学861法学基础综合考研真题及详解北京航空航天大学2014年硕士研究生入学考试试题科目代码：861 科目名称：法学基础综合一、名词解释（本题共20分，每小题5分）1．大陆架2．不成文宪法3．刑法上的紧急避险4．继续犯二、简答题（每小题10分，共50分）1．简述法律行为构成的内在要素。

2．简述立法的基本原则。

3．简述法律解释的原则。

4．列举我国宪法所规定的公民基本权利的类型（至少10种）。

5．简述刑法对自然人刑事责任能力的特别规定。

三、论述题（每小题15分，共60分）1．试论法的要素。

2．论宪法上的平等权。

3．2013年11月，《中共中央关于全面深化改革若干重大问题的决定》正式宣布，将废止劳动教养制度。

请从法理和宪法等角度分析劳动教养制度的不合理之处以及废止劳动教养制度的积极意义。

4．二战后，一些国际人权条约规定了个人的权利和自由，个人还可以在个别国际机构享有一定的申诉权利，某些国家领导人因犯有国际罪行而受到国际刑事司法机构的审判。

个人是不是国际法主体？请对此加以论述。

四、案例分析（每小题10分，共20分）1．1999年3月26日晚被告人李宁、王昌兵与吐逊江（在逃）在阿克苏市一歌舞厅饮酒时，被害人阎世平进入李、王的包间与之攀谈，其间阎提出与李、王合伙挣钱，李宁等人再三追问如何挣钱，阎称准备绑架一市长的儿子。

后被告人李宁、王吕兵乘坐吐逊江驾驶的白色奥拓车将阎拉至阿克苏市团结路一茶园处，李、王等人追问绑架何人，阎世平不说，李宁、王昌兵等遂对阎拳打脚踢。

期间，与被害人阎世平相识的一出租车司机上前劝阻，李、王等人停止了殴打并乘车离开，阎世平乘机躲进该茶园地下室通道处。

后被告人李宁、王昌兵又返回茶园处，找到阎世平，并将其强行拉上车带至西湖后湖堤处。

李宁、王吕兵等人将阎拉下车，拳打脚踢逼问其欲绑架的具体对象，并以此敲诈其钱财。

后被害人阎世平为摆脱李宁、王昌兵等人的殴打，趁其不注意跳入西湖中。

2017－2018 学年第一学期期末试卷学号姓名任课教师成绩考试日期：2018年 1 月23日考试科目：《矩阵理论》（B）注意事项：1、考试8个题目共9页2、考试时间120分钟题目：一、（本题 21 分）二、（本题 10 分）三、（本题 10 分）四、（本题 10 分）五、（本题 15 分）六、（本题 12 分）七、（本题 12 分）八、（本题 10 分）1. （21分）填空（1）A =⎪⎪⎪⎪⎪⎭⎫ ⎝⎛--------1111111111111111, A 的满秩分解为( ).（2）设A =⎪⎪⎪⎭⎫ ⎝⎛i i 20021，则A + = ( ).（3）设A = ⎪⎪⎪⎭⎫ ⎝⎛--011021010, 则 A 的Jordan 标准型J = ( ).（4）设q m q p n m C D C B C A ⨯⨯⨯∈∈∈,,, 则矩阵方程D AXB =相容的充要条件是( ).（5）已知A = ⎪⎪⎪⎭⎫ ⎝⎛432321210, 则 ||A||1 = ( ), ||A||∞= ( ), ||A||F = ( ).（6）设A =⎪⎪⎪⎭⎫ ⎝⎛200120012, k 为正整数，则A k =( ).（7）设三阶矩阵A 的特征值为-1,0,1. 则矩阵A e sin 的行列式是（ ）.2．（10分）设 T 是线性空间3R 上的线性变换，它在3R 中基321,,ααα下的矩阵表示是 ⎪⎪⎪⎭⎫ ⎝⎛-=512301321A . （1）求T 在基321321211,,αααβααβαβ++=+==下的矩阵表示. （2）求T 在基321,,ααα下的核与值域.3．(10分) 设A = ⎪⎪⎭⎫ ⎝⎛2.06.06.02.0, 求证矩阵幂级数∑∞=12k kA k 收敛并求和.4．（10分） 设 A = ⎪⎪⎭⎝-110, 求A 的奇异值分解.5．（15分）已知A = ⎪⎪⎪⎭⎝--5334y x的二重特征值2=λ有两个线性无关的特征向量. （1）求y x ,.（2）求可逆矩阵P ，使AP P 1-为对角矩阵.（3）求A 的谱分解表达式.6．（12分）已知A = ⎪⎪⎪⎭⎫ ⎝⎛-----354113211101，b =⎪⎪⎪⎭⎫⎝⎛-333.（1）用满秩分解求+A . （2）判断方程组Ax = b 是否有解. （3）求Ax = b 的极小范数解或极小最小二乘解.7．(12分) (1) 设n n R A ⨯∈. 证明A 为实对称矩阵当且仅当A 的特征值n λλ,,1Λ为实数，且存在正交矩阵n n R Q ⨯∈，使得},,{1n T diag AQ Q λλΛ=.(2) 设k n n m C B C A ⨯⨯∈∈,, R(A)与R(AB) 分别表示A 与AB 的值域. 证明: R(A)=R(AB)的充分必要条件是存在矩阵,n k C D ⨯∈使得ABD=A.8．（10分）设A = ⎪⎪⎪⎭⎫ ⎝⎛----222132021，求e At ..。

北京航空航天大学考博英语真题2014年(总分100, 做题时间90分钟)Ⅰ. Reading ComprehensionDirections:In this section, there are four texts. After each text, there are five questions marked A, B, C and D. Mark your answers on ANSWER SHEET 1.Text OneA controversy erupted in the **munity in early 1998 over the use of DNA (deoxyribonucleic acid) fingerprinting in criminalinvestigations. DNA fingerprinting was introduced in 1987 as a method to identify individuals based on a pattern seen in their DNA, the molecule of which genes are made. DNA is present in every cell of the body except red blood cells. DNA fingerprinting has been used successfully in various ways, such as to determine paternity where it is not clear who the father of a particular child is. However, it isin the area of criminal investigations that DNA fingerprinting has potentially powerful and controversial uses.DNA fingerprinting and other DNA analysis techniques have revolutionized criminal investigations by giving investigators powerful new tools in the attempt to prove guilt, not just establish innocence. When used in criminal investigations, a DNA fingerprint pattern from a suspect is compared with a DNA fingerprint pattern obtained from such material as hairs or blood found at the scene of a crime. A match between the two DNA samples can be used as evidence to convict a suspect.The controversy in 1998 stemmed from a report published in December 1991 by population geneticists Richard C. Lewontin of Harvard University in Cambridge, Mass., and Daniel L. Hartl called into question the methods to calculate how likely it is that a match between two DNA fingerprints might occur by chance alone. In particular, they argued that the current method cannot properly determine the likelihood that two DNA samples will match because they came from the same individual rather than simply from two different individuals who are members of the same ethnic group. Lewontin and Hartl called for better surveys of DNA patterns methods are adequate. In response to their criticisms, population geneticists Ranajit Chakraborty of the University of Texas in Dallas and Kenneth K. Kidd of Yale University in New Haven, Conn., argued that enough data are already available to show that the methods currently being used are adequate. In January 1998, however, the Federal Bureau ofInvestigation and laboratories that conduct DNA tests announced that they would collect additional DNA samples from various ethnic groupsin an attempt to resolve some of these questions. And, in April, aNational Academy of Sciences called for strict standards and system of accreditation for DNA testing laboratories.SSS_SINGLE_SEL1.Before DNA fingerprinting is used, suspects ______.A would have to leave their fingerprints for further investigationsB would have to submit evidence for their innocenceC could easily escape conviction of guiltD could be convicted of guilt as well该题您未回答:х该问题分值: 1.5答案:C[解析] 本题为推理题。

北京航空航天大学考博英语真题及解析(总分：100.00，做题时间：180分钟)Ⅰ Reading ComprehensionTest One(总题数：1，分数：7.50)Sixty days walking over ice and snow in temperature as low as -45℃, with nothing to keep you company except the occasional polar "bear". This is no small achievement. Only a few people have ever walked to the North Pole unassisted, and if Christina Franco succeeds, she will have earned a place in the history books and met one of the few remaining challenges of exploration left to women.Her 480-mile journey will begin in northern Canada, dragging a sledge that weighs as much as she does. At the end of each day's walking or skiing, she will pitch her tent in subzero temperatures, get into a sleeping bag filled with ice, and attempt to sleep to the unsettling background sounds of howling wind and cracking ice, which may or may not signal the approach of one of those polar bears. "I'll carry a pistol to scare any bears away," says Franco, 42. "The bears that far north won't have had contact with humans, fortunately, so they won't associate me with food, but they will be curious and that's dangerous. If it uses a paw to see what you are, it could damage your tent—or your arm. I imagine I'll have quite a few sleepless nights."Many of the early polar explorers suffered from disease and injuries, and while modem technology (lightweight materials, satellite phones, places on stand-by to carry out rescue missions) has lessened the dangers, it can never make such an inhospitable landscape anything approaching safe. It can take just five minutes for any uncovered skin to become frostbittenand, once the sun has risen, Franco will only be able to remove her sunglasses inside her tent, otherwise the intensity of the sunlight reflecting off the snow would cause snow blindness. Just to heighten the danger, the cold will slow down her brain functions, so it will be more difficult to make split-second decisions in the event of a sudden crisis.She will use about 8,000 calories a day, losing nearly half a kilogram every 24 hours. "The problem is that the human body can only take on about 5,500 calories a day," she says. "So you have to fatten up before you set off or you'll run out of energy." Franco is currently trying to put on 19 kilos. She may complain about not fitting into any of her dresses, but when Franco weighs herself in front of me and finds she's lost one kilo rather than gained two, as she'd expected, she's very upset. "I hope my scales are wrong because, if not, I've lost weight," she says, reaching for one of many bars of chocolate lying around her kitchen.1. What does the writer say about the history of exploration? ______（分数：7.50）A.Walking to the North Pole used to be considered easier than other journeys.B.No woman has ever completed the journey to the geographic North Pole.C.Female explorers have already done most of the world's difficult journeys. √D.Franco is already an important historical figure for her previous journeys.解析：根据第一段中的“Only a few people have ever walked to the North Pole unassisted, and if Christina Franco succeeds, she will have earned a place in the history books and met one of the few remaining challenges of exploration left to women.”可知，只有少数人曾独自走到北极，如果克里斯蒂娜·佛朗哥成功了，她将在史书中占有一席之地，完成为女性留下的尚未完成的为数不多的探险挑战之一。