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1、数学与应用数学高等代数第一学期期末考试试卷（闭卷A 卷）一、单项选择题（每小题2 分，共 10 分）1.若123123123aaabbbmccc，则111122223333253253253acbbacbbacbb().A30m B.-15mC 6m D.-6m2.n阶矩阵 A可逆的充分必要条件是().AA=0B.r（A）nC.A是满秩矩阵D.A是退化矩阵3下列说法不正确的是().A任何一个多项式都是零次多项式的因式B.如果 f(x)g(x)，g(x)h(x)，则 f(x)h(x)C.如 A 是n阶矩阵，则()()()()AEAEAEAED.如 A 是n阶矩阵，则mkkmA AA A4.设向量
2、组,线性无关，,线性相关，则().A一定能由,线性表示B.一定能由,线性表示C.一定不能由,线性表示D.一定不能由,线性表示5.对于n元方程组，下列命题正确的是().A如果0Ax只有零解，则 Axb也只有零解B.如果0Ax有非零解，则 Axb有无穷多解C.如果Axb有两个不同的解，则0Ax有无穷多解D.Axb有唯一解的充分条件是()rnA二、填空题（每空2 分，共 20 分）1.若 A=321?（4,5,6），则 A=.2.f(x)=1-xx34，则）x（f）5（=3p(x)是不可约多项式，对于任一多项式f(x)，已知 p(x)f(x)，则（p(x),f(x)）=.4.已知A=4521-011
3、13011-2101，则A12-A22+A32-A42=_ .5.设 A=300020001，（1A）*是1A 的伴随矩阵，则（1A）*=6.若(1,0,5,2)T1,(3,2,3,4)T2,3,1,3Tt3线性无关，则 t .7.设 =（0,1，-1），=（1,0,-2）,则向量组 ,的秩=.8.设 f(x)Rx,deg f(x)2,且 f(1)=1，f(-1)=2，f(2)=0,则 f(x)=.9.一个n阶矩阵是非退化的充分必要条件是它的秩=.10.设 3 阶矩阵A的伴随矩阵为*A，A=1，则-2*A=三、计算题（每小题10 分，共 50 分）1.问 k,m,n 满足什么条件时,x2+kx
4、+1 能整除 x3+mx+n.2.计算行列式0001200034123760458700698的值.3设 A=120130004，求1A4.求齐次线性方程组1234123412340253207730 xxxxxxxxxxxx的基础解系和通解5.设,4321,6063324208421221bA求矩阵 A 及矩阵),(bAA的秩.四、证明题（每小题10 分，共 20 分）1.设列矩阵TnxxxX),(21满足,1XXTE为 n 阶单位矩阵,2TXXEH证明 H是对称矩阵.2.已知123,线性无关，证明12.23,23,123线性无关.高等代数（一）（闭卷 A卷）答案一、单项选择题（每小题2 分
5、，共 10 分）1.D 2.C 3.A 4.B 5.C 二、填空题（每空2 分，共 20 分）1.0；2.0；31；4.0；5.210003100061；6.21；7.2；8.31-x23x613-2；9.n；10.-8.三、计算题（每小题10 分，共 50 分）1.解：用 x 2+kx+1 除 x3+mx+n，商式是 x-k 余式是（k2+m-1）x+（k+n）4 分所以 x3+mx+n=（x 2+kx+1）（x-k）+（k2+m-1）x+（k+n）x 2+kx+1 整除 x3+mx+n的充要条件是（k2+m-1）=0 且（k+n）=0 4 分n=-k，m=1-k2 2 分2.解：文档编码:
6、CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码
7、:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编
8、码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档
9、编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文
10、档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9
11、文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B
12、9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B92 300012120000003434000112376761230458787
13、04500698980061231204534006240 4 分 2 分此答案仅做参考，因为计算方法不止一种，对于其它做法全对的给满分，不全对者酌情给分！3解：令A=2100AAA1=4,A2=1213 4 分（4-1）=41，32-1-112131-4 分1A=32-01-100041 2 分此答案仅做参考，因为计算方法不止一种，对于其它做法全对的给满分，不全对者酌情给分！4.解：对系数矩阵A作初等行变换，变为行最简矩阵，有111125327731111107540141081111075400002310775401770000A 4 分得13423423775477xxxxxx，4 分
14、所以基础解系为12237754,771001 4 分文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H
15、1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10
16、H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D1
17、0H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D
18、10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2
19、D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E
20、2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9通解为121 122
21、34xxxccxx，12,c cR 2 分5.解：46063332422084211221A141312322rrrrrr13600512000240011221 4 分2423232rrrrr100005000001200112213425rrr00000100000120011221 4 分.3)(,2)(ArAr 2 分五、证明题（每小题10 分，共 20 分）证明THTTXXE)2(TTTXXE)(2 4 分TXXE2,H 4 分由对称矩阵的定义可知H是对称矩阵.2 分2.证明：设112223312323,，则123123201,311011 4 分令123,B，123,A，20131
22、101 1k，则上式可写为 BAk，而2013111001 1k，所以 k 可逆 4 分所以 RRBA，又知123,线性无关，所以12.23,23,123线性无关。2 分此答案仅做参考，因为计算方法不止一种，对于其它做法全对的给满分，不全对者酌情给分！文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档
23、编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文
24、档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9
25、文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B
26、9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10
27、B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A1
28、0B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A
29、10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7
30、A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z
31、7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4
32、Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G
33、4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10
34、G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR1
35、0G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9文档编码:CJ3U5E2D10H1 HV1U4L7Y8C1 ZR10G4Z7A10B9