26..5特征值与特征向量矩阵的简单应用.pdf

《26..5特征值与特征向量矩阵的简单应用.pdf》由会员分享，可在线阅读，更多相关《26..5特征值与特征向量矩阵的简单应用.pdf（11页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、1/11 本资料来源于七彩教育网http:/ 26.5 特征值与特征向量矩阵的简单应用【知识网络】1、矩阵特征值与特征向量的定义，能从几何变换的角度说明特征向量的意义；2、会求二阶方阵的特征值与特征向量只要求特征值是两个不同实数的情形）；3、了解三阶或高阶矩阵；4、矩阵的应用。【典型例题】例 1：1）、已知5a，且(4,)an，则 n 的值是 ）A3 B 3 C 3 D不存在2z4sV2AHVW 答案：C。解读：5422na，解得 n=3。2z4sV2AHVW A、931 B、1031 C、1131 D、1231答案：C。解读：1010113 0333 030 1110 11。3）设某校午餐有

2、A、B 两种便当选择，经统计数据显示，今天订 A 便当的人，隔天再订A 便当的机率是35；订 B 便当的人，隔天再订 B 便当的机率为45，已知星期一有40%的同学订了A 便当，60%的 同 学 订 了 B 便 当，则 星 期 四 时 订A 便 当 同 学 的 比 率 为）2z4sV2AHVW 2/11 A、208625 B、209625 C、210625 D、211625答案：D。解读：设 M=31552455，则 M3473922111251255625788634141251255625。(+3-(-25(-2=2+2-8=0 解得，矩阵 M的两个特征值1=-4，2=2。5）一实验室培养

3、两种菌，令na和nb分别代表两种培养菌在时间点 n 的数量，彼此有如下的关系112(),2(0,1,2)nnnnnaabbb n，若二阶矩阵A=bc da满足n+bn+3caAnbna，(-3-(-25(-2=2-2-8=0 解得，矩阵 M的两个特征值1=4，2=-2 设属于特征值1=4 的特征向量为yx，则它满足方程：(1+1x+(-2y=0 即：y=0 也就是 5 x-2y=0 则可取52为属于特征值1=4的一个特征向量设属于特征值1=-2 的特征向量为yx，则它满足方程：(2+1x+(-2y=0 即：y=0 也就是 x+2y=0 则可取12-为属于特征值2=-2 的一个特征向量综上所述：

4、M=251-32有两个特征值1=4，2=-2，属于1=4 的一个特征向量为52，属于2=-2 的一个特征向量为12-。例 4：已知：矩阵 M=251-32，向量=161求 M3答案：由上题可知1=51，2=12-是矩阵M 分别对应特征值1=4，2=-2的两 个 特 征向量，而1与2不共 线。又=161=351+12-=31+22z4sV2AHVW 文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5

5、I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X

6、5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10

7、X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y1

8、0X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y

9、10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8

10、Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ

11、8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O44/11 ABCDM3=M331+2）=3 M31+M32 =3131+232=34351+，b(1，2，则 3a2b的坐标是 (A(7，1 B(7，1 C(7，1 D(7，1 答案：B。2矩阵4 22 1的特征值是 ）2z4sV2AHVW A、0和 5 B、0 和5 C、1和 4 D、1和4 答 案：A。解 读：由 已

12、 知2()(4)(1)450f，解 得120,5。3下图为一个网络，则一级路矩阵为 ）2z4sV2AHVW A、0 1 1 21 0 1 01 1 0 02 0 0 0 B、0 1 2 21 0 1 22 1 0 02 2 0 0 C、0 2 2 22 0 2 12 2 0 02 1 0 0 D、0 2 2 22 0 2 22 2 0 22 2 2 0答案：A。4矩阵 A=1 42 3的特征多次式为。答案：245。解读：21 -4()45-2 -3f。5设 A 是一个二阶矩阵，满足A11300，且 A11633，则A=。答案：3 10 6。解读：设 A=bc da，则3,0,36,318,3,

13、1,0.6acabcdabcd。6矩阵 M=1 23 2的所有特征向量为。文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:

14、CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码

15、:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编

16、码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档

17、编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文

18、档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4

19、文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O

20、45/11 答案：k23和k1,(0)1k。解读：已知2()(1)(2)6340,f121,4，对应的特征向量为11和23，故所有的特征向量为：k23和 k1,(0)1k。7已知点列*(,)()nnnPxynN满足1124nnnnnnxxyyxy，且111,2xy，则P4坐标为。答案：2，6）。解读：23232(2)42()(43)4(2)4434()(43)nnnnnnnnnnnnnnnnnnnnnxxyxyyxyxyyxyxyxyyyxy即3344nnnnnnxxyyxy，故334 1-4 -1nnnnxxyy，又111,2xy，4 112-4 -126，即 P42，6）。8求矩阵 A=3

21、 10 -1的特征值与特征向量。答案：矩阵A 的特征多项式()(3)(1),3f或1，其相应的特征向量分别为10和14。9已知 ABC的坐标分别为A1，1）、B3，2）、C 其坐标形式分别为：y x=11+t 12 (tR 由，直线 AB的坐标形式方程可化为：t1y2t1x消去 t 后得普通方程为：x-2y+1=0 所以所求 高 为C到 直 线AB的 距 离，设 为h,则：h=文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3

22、V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X

23、3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7

24、X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG

25、7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 H

26、G7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10

27、HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10

28、 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O46/11=5。2z4sV2AHVW 10假设某地只有甲乙两家工厂生产并贩卖某一种产品每一年甲工厂的顾客中有34转向乙工厂购买此产品，只有14仍然向甲工厂购买；而乙工厂的顾客中有13转向甲工厂购买，其余23的顾客仍然向乙工厂购买，请问一年、二年、三年后，甲乙两家工厂的市场占有率为何？2z4sV

29、2AHVW 答案：设甲乙两工厂目前市场占有率为00,xy，其中001,xyn年后甲乙两工厂市场占有率分别为,nnxy第一年甲工厂的市场占有率1001143xxy，乙工厂的市场占有率1003243yxy，令 A=11433243，Xn=nnxy，则可用 AX0=11433243nnxy=11xy=X1表示上述的关系第二年甲工厂的市场占有率2111143xxy，乙工厂的市场占有率2113243yxy，则 AX1=1143324311xy=22xy=X2AXn=Xn+1,根据上述的关系：2312330()()nnnnnnXAXA AXAAXA XA X所以 X2=000000151115114836

30、48363325332548364836xyxyxy，X3=000000177133177133+432432432432255299255299432432432432xyxyxy【作业本】A 组1 对 于 一 个 二 阶 矩 阵A，下 列 说 法 正 确 的 是 ）2z4sV2AHVW A、它的特征向量是唯一的 B、它的特征向量有且只有两个2122|14221|文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5

31、 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M

32、5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4

33、M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W

34、4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2

35、W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V

36、2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3

37、V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O47/11 ABCC、它的特征向量有无穷多个D、它的特征向量由它的特征值来确定答案：D。2设 M=1 -11 1，则 M50=）2z4sV2AHVW A、25250 -22 0 B、2525-2 00 2 C、25252 00 -2 D、25250 2-2 0答 案：A。解 读：M2=0 -22 0，M4

38、=4 00 -4，M50=2425412224252 02 00 -2()0 20 22 0MM。3假设每市每年有5%的人口移入市区，而市区每年有3%的人口移入郊区，且无其它地方的人口移入或移出，则市区与郊区的人口占比可用矩阵表示 ）2z4sV2AHVW A、0.95 0.030.05 0.97 B、0.03 0.950.97 0.05 C、0.05 0.950.03 0.97 D、0.05 0.970.03 0.95答案：A。4矩阵 A=1 12 -3的特征值为。答案：16。解读：由已知2()(1)(3)2250f，解得16。5如图所示的是 A，B，C 三个城市间的交通情况，则二级路矩阵为。

39、答案：5 2 42 8 24 2 5。解读：由题意知，一级路矩阵M=0 2 12 0 21 2 0，则二级路矩阵 N=M2=5 2 42 8 24 2 5。文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC

40、5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:C

41、C5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:

42、CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码

43、:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编

44、码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档

45、编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文

46、档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O48/11 6已知 M=1 -23,-2 11，试计算20M答案：矩阵M 的特征多次式为212()(1)40,3,1f，对应的 特 征 向 量 分 别 为11和11，而11211，所 以2020202020113232(1)1132M7为了保密，军中经常针对不同的军事行动而更改密码，今若约定以24阶矩阵中每一列的数字和之个位数字代表更改后的密码，例如3 8 2 54 8 6 7所代表的密码为7682。而且为了确保密码在传送过程中，不被敌方所窃取，因而作了加密动作，即将所要传送的密码之24阶矩阵乘以固定矩阵X=2

47、13 1，然后将所得出的24阶矩阵传送给对方，当对方收到传送过来的24阶矩阵后再进行解密的动作例如：原始的矩阵为A，先经过 XA=B之运算后，再将B 传送出去）。今若对方收到的24阶矩阵为15 4 22 722 4 30 8，问原始密码为何？2z4sV2AHVW 答案：由题意知：A=1-1 115 4 22 77 0 8 13 -222 4 30 81 4 6 5XB，原始密码为 8446。8有一个心理学家做了如下的老鼠实验：于前次的实验中，走向右边的老鼠中，有80%在下次实验中仍走向右边；走向右边的老鼠中，有 60%在下次实验中走向右边。1）试求其转移矩阵；2）如果在第一次实验中有50%的老

48、鼠走向右边，试求在第三次实验，有多少老鼠走向右边？2z4sV2AHVW 答案：1）M=0.8 0.60.2 0.4；2）M20.50.76 0.720.50.740.50.24 0.280.50.26，在第三次实验中，有74%的老鼠走向右边。文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC

49、5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:C

50、C5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码:CC5X7U10W5V10 HG7X3V2W4M5 ZZ8Y10X5I1O4文档编码: