11高代试题A

-1-重庆理工大学考试试卷2011～2012学年第1学期班级学号姓名考试科目高等代数[I]A卷闭卷共4页····································密························封························线································学生答题不得超过此线题号一二三四五六七八九总分总分人分数一、选择题(每小题2分，共20分)得分评卷人1.下列说法不正确的是（）A.任何数域都包含有理数域；B.两个数域的交还是数域；C.数环一定是数域；D.任何数域都包含0和1.2.设()fx是三次实系数多项式，则()fx（）A.至少有一个有理根B.存在一对非实共轭复根C.有三个实根D.至少有一个实根3．下列对于多项式的结论不正确的是（）A.如果)()(,)()(xfxgxgxf，那么)()(xgxf；B.如果)()(,)()(xhxfxgxf，那么))()(()(xhxgxf；C.如果)()(xgxf，那么][)(xFxh，有)()()(xhxgxf；D.如果)()(,)()(xhxgxgxf，那么)()(xhxf.4．设有行列式121243113，则3132332M3AA()A.0B.4C.-4D.35.设*A为4阶方阵A的伴随矩阵且2A，则*2-A（）A.42B.72C．72D.526.设线性方程组Axb的增广矩阵是103101210121，则Axb解的情况是（）A.有唯一解B.无解C．有三个解D.有无穷多个解7.设非齐次线性方程组Axb，其中A为n阶方阵，则以下结论不正确的是（）A.若nAr)(，则Axb一定有解；B.若()rArn，则Axb有解且有nr个自由未知量；C.若方程组有解，则有惟一解；D.若系数行列式0A，则方程组有惟一解.8.设A为数域F上的n阶方阵，满足220AA，则下列矩阵哪个可逆（）A.AB.AIC．AID．2AI9.设A、B均为n阶方阵，1OC=-2TAOB，则|C|()A.2-12|A|||nB（）；B.1(2)|A|||nB；C．T2|A|||B；D.-12|A|||B.10.若矩阵A，B满足ABO，则（）重庆理工大学考试试卷2011～2012学年第1学期-2-班级学号姓名考试科目高等代数[I]A卷闭卷共4页····································密························封························线································学生答题不得超过此线A.AO或BO；B.AO且BO；C.AO且BO；D.以上结论都不正确二、(8分)得分评卷人给定多项式()fx、()gx、()hx，（1）若((),())1fxhx，且((),())1gxhx，证明：(()(),())1fxgxhx；（2）若((),())1fxgx，证明：((),())1nfxgx三、(10分)得分评卷人设1x，2x，3x为多项式32()232fxxxx的根，应用初等对称多项式表示对称多项式的方法求222222123121321233132(,,)fxxxxxxxxxxxxxxx的值.四、(10分)得分评卷人计算n阶行列式12334100001110000110000001000011nnnnaaaaaDaaa重庆理工大学考试试卷2011～2012学年第1学期班级学号姓名考试科目高等代数[I]A卷闭卷共4页-3-····································密························封························线································学生答题不得超过此线五、(12分)得分评卷人为何值时，线性方程组12341242343212331xxxxxxxxxx有解，有解时，求出一般解.六、(10分)得分评卷人设n阶方阵A满足223nAAIO，证明：2nAI可逆，并表示1(2)nAI重庆理工大学考试试卷2011～2012学年第1学期班级学号姓名考试科目高等代数[I]A卷闭卷共4页····································密························封························线································学生答题不得超过此线七、(10分)-4-得分评卷人已知3阶方阵111121113A，求1(4)AA.八、(10分)得分评卷人设矩阵311031103A，121032B，且12AXABX，求X九、(10分)得分评卷人已知矩阵2100110012251113A，求1A