高等代数期末考试(A)卷.doc

华南农业大学期末考试试卷（A卷）2010学年第一学期 考试科目： 高等代数 考试类型：（闭卷）考试时间：120 分钟学号 姓名 年级专业 题号一二三四五总分得分评阅人一、填空题（35=15分）1、设是阶方阵，均为线性方程组的解，且，则的秩 ；2、已知，则 ；3、若为三阶方阵，为的伴随矩阵，且|=，则 ；4、如果向量，可以由唯一地线性表示，那么满足：；5、设是多项式的二重根，则，。二、判别题（25=10分）（请在正确的小题对应的括号内打“”，否则打“”） 6、如果是多项式和的一个最大公因式且，那么和唯一。（ ）7、设为阶方阵，若，且，则。（ ）8、若矩阵有一个非零r阶子式，则。（ ）9、含有个未知数的线性方程组有解的充分必要条件是它的系数矩阵的秩等于。（ ）10、若是正定矩阵，那么也是正定矩阵。（ ）三、单项选择题（35=15分）11、若集合（这里是实数集）是数域，则应满足条件（ ）。（A）是整数 （B）是无理数 （C）是有理数，是实数 （D）是任意实数12、初等矩阵（ ）（A）所对应的行列式的值等于 （B）都是可逆阵 （C）相乘仍为初等矩阵 （D）相加仍为初等矩阵13、设, 两个维向量组：(1)， (2) 下述正确的是（ ）（A）若(1)可由(2)线性表出, 则(1)线性相关；（B）若(1)可由(2)线性表出, 则(1)线性无关；（C）若(1)可由(2)线性表出, 则当(2)线性无关时, (1)线性无关；（D）若(1)可由(2)线性表出, 则仅当(2)线性相关时, (1)线性相关。14、设数域，多项式，则（ ）（A）在上不可约当且仅当在上不可约；（B）在上无重因式当且仅当在上无重因式；（C）在上有根当且仅当在上有根；（D）在上有非平凡因式当且仅当在上有非平凡因式。15、设有一个非零的级子式，则必有 （ ）（A）秩() （B）秩() （C）秩() （D）必有一个非零的级子式四、解答题（75=35分）16、设， ，求 。 17、求下列向量组的秩及一个极大无关组，并用该极大无关组表示余下的向量：。18、线性方程组 ，当为何值时，方程组有唯一解，无解，无穷多解？并用基础解系表示通解。19、用逆矩阵求解矩阵方程 。20、作非退化线性变换把实二次型化为实数域中的规范形。五、证明题（25分）21、证明：若，且为与的一个组合，则是与的一个最大公因式。（7分）22、向量组线性相关的充要条件是中至少有一个向量可以由其他向量线性表示。（6分）23、证明：秩秩+秩。 （6分）24、设是两个数域，证明：的交集也是数域。（6分）他为分公司培养出了鲁付凯、孙垚、徐童晨、肖大鹏四名测量员，他们现在个个都能独当一面。当突然得知自己面临死亜时，人们也许会想“为什么恰巧是我”，会怆恨命运癿天平为何没有偏向自己。猝丌及防癿“死亜判决书”桌上放着一本白色封面的特殊书籍，上面写着中华人民共和国监察法。金色的国徽熠熠闪光，鲜艳得足以让人感受到一种责任就在心底深处缓缓晕开warmly, welcoming us to join forces, and saw my fill of . People traveled a long journey around the life was hard work and passion has always been high. Six months later, when we moved to new, I suddenly suffering from malaria, joint pain, reduced mobility, which often eat salted vegetable soup with six months, poor nutrition, sleep shop, cold wet bone a lot. Comrades, according to report to their superiors, Special Branch Director Guo Zeming Wuzhen to appoint expatriates hired a boat ship to accompany me back to the village. When leaving, comrades warm farewells, coming, earnestly exhort, hope that the early return of the illness. 2, the second year of the war all fall into enemy hands, the main town in Wujiang, diwei groups have been set up, shameless traitor, thief as you recognize, while fiddling with the people suffered. But remoteness along the Taihu Lake, a number of sporadic anti-Japanese guerrilla in the local activities. After the fall of song Ling Zhen, Wujiang County Government moved in Tomb in Nan Xiang Zhang Aocun, a market stood in the vicinity of the temple. Chang Shen Liqun, shengze person Secretary and section chief Shen Zhian, zhenze who Niu Xiqing, the Chief of the second section, grave; the County Education Bureau Director Zhao Ziquan; the County Party Secretary Zhou Shihong; armed standing directly under Captain Huang Jun. Also appointed district head, flow working separately in each country. April 1939 sent to Mr Shen Zhian, about meeting I went to pier of Fame, rank was zhenze poem field primary school, later Yuying high school Council, more familiar in the past and liked, so I gladly obey. Rank wants me in there to help do some paperwork, and Chang Shen Liqun, to recommend, so I was appointed as the first clerk in charge of relevant written work in education. County Government departments the staff scattered around the farmhouse,the vast numbers of officers and men to resist invasion, defying the enemy showed that dare, dare, dare to fight Chong of the national spirit will forever published people in Jiangsu, Zhejiang and neighboring areas of the history of the war. (IX) Recalling old Jaksa of the war 1, in July 1937, I graduated from zhenze Yuying secondary school. From August 1 to 3rd, Zhejiang University State resistance to Central Wuhan and Zhejiang, the University joint entrance examination, 4th home waiting for admission. However, less than 10 days, have taken place in Shanghai 83 or 13 incident, several months after the fight to zhenze, Cang depression, home on November 17, and dreams come to nothing. At that time, I and my mother couldnt escape strict sister home. Spring of 1938, I heard that wuzhenxiang there is the regular guerrilla, prepared to carry out guerrilla warfare against the enemy, destroy the traitors. In early June, compatriot Wang Zhuoyun doctors joined zhenze secondary two student Xu Jiazheng and Yang Yaozong visits. Talk began that, Wang has been in the guerrilla army doctor, he went about the three of us joined the army. I was depressed when smelling this surging, itch, but mother block, news release, panic said behind education, quickly packed, hire boats, led by Wang Zhuoyun went to the army. Boat Czech Republic sailed between rural water village Wuzhen River twisting inside the harbour connected to the duckweed, on both sides of the mulberry is lush. Near the station, from time to time post questioning is fortunate to have Dr Wang guided pass one another off. Command received us第5页共6页