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1、05秋05级《代数与几何》期末试卷（此卷满分50分）一、填空题（每小题2分，共10分）1.在空间直角坐标系中，点到直线的距离为.2.若阶方阵满足，，则.3..5.若是方阵的一个特征向量，则，是的全部特征值.二、选择题（每小题2分，共10分）1.设是矩阵，对于线性方程组，下列结论正确的是(A)若，该方程组有无穷多解.(B)若，该方程组有解.(C)若，该方程组有唯一解.(D)若，该方程组无解.【】2.设有阶矩阵，维列向量组(I);(II)，则(A)若（I）相关，则（II）相关.(B)若（II）相关，则
2、（I）相关.(C)若可逆，则（II）无关.(D)若（II）无关，则可逆.【】3.坐标面上的双曲线绕轴旋转一周，所生成的旋转曲面的方程为.(A).(B).(C)(D).【】4.(A).(B).(C).(D).【】officiallyestablishedonJuly1,2013,Yibincity,formerlyknownasthebus,integratedoriginalrongzhoubuscompanyinYibincityandMetrobuscompany,formedonlyinYi
3、bincityofaState-ownedpublictransportenterprises,thecompanyconsistsofoneortwo,thirdDivision.Integrationofpublictransportservicesisnotyetestablished第9页（共6页）(A)(B)(C)(D)【】officiallyestablishedonJuly1,2013,Yibincity,formerlyknownasthebus,integratedorigina
4、lrongzhoubuscompanyinYibincityandMetrobuscompany,formedonlyinYibincityofaState-ownedpublictransportenterprises,thecompanyconsistsofoneortwo,thirdDivision.Integrationofpublictransportservicesisnotyetestablished第9页（共6页）三、（本题5分）当等于何值时，方程组无解，有唯一解，有无穷多解？当有
5、无穷多解时，写出通解.四、（本题5分）求直线在平面上的投影直线的方程.officiallyestablishedonJuly1,2013,Yibincity,formerlyknownasthebus,integratedoriginalrongzhoubuscompanyinYibincityandMetrobuscompany,formedonlyinYibincityofaState-ownedpublictransportenterprises,thecompanyconsistsofon
6、eortwo,thirdDivision.Integrationofpublictransportservicesisnotyetestablished第9页（共6页）五、（本题5分）已知与相似，其中，.（1）求；（2）求一个与相似的对角阵；（3）求的特征多项式.officiallyestablishedonJuly1,2013,Yibincity,formerlyknownasthebus,integratedoriginalrongzhoubuscompanyinYibincityandMet
7、robuscompany,formedonlyinYibincityofaState-ownedpublictransportenterprises,thecompanyconsistsofoneortwo,thirdDivision.Integrationofpublictransportservicesisnotyetestablished第9页（共6页）officiallyestablishedonJuly1,2013,Yibincity,formerlyknownasthebus,inte
8、gratedoriginalrongzhoubuscompanyinYibincityandMetrobuscompany,formedonlyinYibincityofaState-ownedpublictransportenterprises,thecompanyconsistsofoneortwo,thirdDivision.Integrationofpublictransportservicesisnotyetestablished第9页（共6页）officiallyest
