用Matlab学习线性代数

1、用Matlab学习线性代数线性方程组与矩阵代数实验目的：熟悉线性方程组的解法和矩阵的基本运算及性质验证。Matlab 命令：本练习中用到的 Matlab 命令有：inv，floor，rand，tic，toc，rref，abs， max，round，sum， eye，triu，ones，zeroso本练习引入的运算有：+，-，*，。其中+和-表示通常标量及矩阵的加 法和减法运算；*表示标量或矩阵的乘法；对所有元素为实数的矩阵，运算对应 于转置运算。若A为一个nxn 非奇异矩阵(det!=0)且B为一个nxr矩阵，则运 算A B等价于A-1B。实验内容：用Matlab随机生成4x4的矩阵A和B。求

2、下列指定的C,D,G,H，并确定 那些矩阵是相等的。你可以利用Matlab计算两个矩阵的差来测试两个矩阵 是否相等。C=A*B,D=B*A,G=(A *B)，H=(B *A) C=H;D=G;C=A *B，D=(A*B)，G=B *A，H=(B*A) C=H;D=G;C=inv(A*B),D=inv(A)*inv(B),G=inv(B*A),H=inv(B)*inv(A)C=inv(A*B) ),D=inv(A *B ),G=inv(A )*inv(B ),H=(inv(A)*inv(B) (4)中无相等的令n=200，并使用命令A=floor(10*rand(n);b=sum(A)z=one

3、s(n,1);注释：(n行一列全为1的矩阵)生成一个nxn矩阵和两个Rn中的向量，它们的元素均为整数。(因为矩阵和 向量都很大，我们添加分号来控制输出。方程组Ax = b的真解应为z。为什么？【A中的每一行的元素之和 正好等于对应b的每一列，故z为其一解，又det不等于0，RA=RAb=n，故z为其解】试说明，可在Matlab中利用” ”运算 或计算A-1，然后用计算A-ib来求解。比较这两种计算方法的速度和 精度。我们将使用Matlab命令tic和toc来测量每一个计算过程消耗 的时间。只需要用下面的命令：tic,x=Ab； toctic,y=inv(A)*b; toc哪一种方法更快？tic

4、,x=Ab ；更快！为了比较这两种方法的精度，可以测量求得的解x和y与真解z接近 的程度。利用下面的命令：max(abs(x-z)max(abs(y-z)哪种方法的到的解更精确？ max(abs(x-z)= 4.0168e-013更精确！ max(abs(y-z) = 6.1107e-013用 n=500 和 n=1000 替换(1)中的n。如(1)结果一样!令A=floor(10*rand(6)。根据构造，矩阵A将有整数元。将矩阵A的第六 列更改，使得矩阵A为奇异的。令B=A，A(:,6)=-sum(B(1:5,:) 设x=ones(6,1),并利用Matlab计算Ax。为什么我们知道A必为

5、奇异的？【因化简列，列成比例】试说明。通过化为行最简形来判断A是奇异的。令B=x*1:6，乘积AB应为零矩阵。为什么？【因A的每一行的前 五个元素之和等于第六个元素的相反数，且在A上的每一行的元素同 乘以相同的数，则仍等于0】试说明。用Matlab的*运算计算AB进 行验证。 令 C=floor(10*rand(6)和 D=B+C,尽管C D，但乘积 AC 和 AD 是 相等的。为什么？试说明。计算A*C和A*D,并验证它们确实相等。【此处 B 为令 B=x*1:6; A 为 A(:,6)=-sum(B(1:5,:)】由于 A*B=0;故 AC=AD; A(B+C)=AB+AC;采用如下方式构

6、造一个矩阵。令B=eye(10)-triu(ones(10),1),参见最后附表二:为什么我们知道B必为非奇异的？【上三角矩阵的行列式的值等于对角线上的元素相乘】令 C=inv(B)且 x=C(:,10),现在用B(10,1)=-1/256将B进行微小改变。利用Matlab计算乘积Bx。由这个计算结果，你可以得出关于新矩阵B的什么结论？【化简此时B,得行最简式，RB=910，可以得出B的第10列(从19行)与x互为相反 数，且都是2的指数幂数，且第十行为0，】它是否为奇异的？【是】试说明。用Matlab计算它的行最简形。生成一个矩阵A：A=floor(20*rand(6)并生成一个向量b：B=

7、floor(20*rand(6,1)-10因为A是随机生成的，我们可以认为它是非奇异的。那么方程组Ax = b应有唯一解。用运算“”求解。用Matlab计算A b的行 最简形U。比较U的最后一列和解x,结果是什么？【相等】在 精确算术运算时，它们应当是相等的。为什么？【行最简式中可写 出对应元素的实际含义，对应处的未知元就等于最后的数】试说明。 为比较他们两个，计算差U(:,7)-x或用format long考虑它们。现在改变A,试它成为奇异的。令A(:,3)=A(:,1:2)*4 3【第一 列乘以4加上第二列乘以3替换到第三列上】，利用Matlab计算 rref(A b)。方程组Ax = b

8、有多少组解？【无解】试说明。【RARAB】令y=floor(20*rand(6,1)-10且c=A*y,为什么我们知道方程组 Ax=c必为相容？的？【x此时必有一解y,故为相容的】试说明。 计算A c的行最简形U。方程组Ax = b有多少组解？【无穷多解】 试说明。【RA=RA c6】由行最简形确定的自由变量应为x3。通过考察矩阵U对应的方程 组，可以求得x3 =0时所对应的解。将这个解作为列向量w输入 Matlab中。为检验Aw = c，计算剩余向量c - Aw。 令U(:,7) = zeros(6,1)。矩阵U应对应于Ia 10】的行最简形。用U求 自变量x3 = 1时齐次线性方程组的解(

9、手工计算)，并将你的结果 输入为向量Z。用A*Z检验你的结论。令v = w + 3* z。向量v应为方程组Ax = c的解。为什么？试说明。用Matlab计算剩余向量来验证v为方程组的解。在这个解中，自 由变量X3的取值是什么？【x3 =3如何使用向量w和z来求所有可能的方程组的解？【v=w+n*z,其中n为任意实数】试说 明。考虑下图：确定图的邻接矩阵A,将其输入Matlab;计算A2并确定长度为2的路的条数【72】，其起止点分别为：AA2+A 中的数值之和，数字表示有几种路径，具体看程序】 计算A4、A6、As并回答(2)中各种情况长度为4、【368】6、2362 8、15800的路的条数

10、。试推测什么时候从顶点Vi到Vj没有长度 为偶数【即为0】的路。【i=1, j=6; i=2,j=5; i=3,j=6或8;i=4,j=7;i=5,j=8;i=6,j=1 或 3;i=7,j=4;i=8,j=3 或 6; 计算A3、A5、A7并回答(2)中各情况长度为3、154 5、9227 6098的路的条数。你由(3)得到的推测对长度为奇数的路是否成立？【不成立】，试说明【见程序】。推测根据i+j+k的奇偶性，是否存在长度为k的路。【若i+j+k为偶数，不存在；相反，则存在】 【路径见程序】如果我们在图中增加边V3,V6，V5,V8，新图的邻接矩阵B可首先 令 B=A，然后令 B(3,6)

11、 = 1, B(6,3) = 1, B(5,8)=1, B(8,5)=1，对 k=2,3,4,5计算Bk。(4)中的推测在新的图形中是否还是成立的？【不 成立】见程序】在图中增加V6，VJ，并构造得到的图的邻接矩阵C，计算C的幂次， 并验证你在(4)中的推测对这个新图是否仍然成立。【不成立】【见程序】7 .令A=magic(8),然后计算其行最简形。使得首1对应于前三个变量x ,x ,x ,123且其余的五个变量均为自由的。(1)令c=1:8，通过计算矩阵Ac的行最简形确定方程组Ax=c是否相容。方程组是相容的吗？【不相容】试说明。【RA C-Dans =2.2376e-001 4.7289e

12、-001-6.3633e-001 -3.0354e-001-1.7227e-001 -1.1938e-001-8.7955e-001 -6.5016e-001 C-Gans =2.2376e-001 4.7289e-001-6.3633e-001 -3.0354e-001-1.7227e-001 -1.1938e-001-8.7955e-001 -6.5016e-001 C-Hans =00000000000000001.3979e+000 1.3204e+0002.2485e-002 -1.5056e-0012.9484e-001 2.3624e-0018.0370e-002 -2.1506

13、e-0011.3979e+000 1.3204e+0002.2485e-002 -1.5056e-0012.9484e-001 2.3624e-0018.0370e-002 -2.1506e-001 D-G ans =0000000000000000 D-H ans =-2.2376e-001 -4.7289e-001 -1.3979e+000 -1.3204e+0006.3633e-001 3.0354e-001 -2.2485e-002 1.5056e-0011.7227e-001 1.1938e-001 -2.9484e-001 -2.3624e-0018.7955e-001 6.501

14、6e-001 -8.0370e-002 2.1506e-001 G-Hans =-2.2376e-001 -4.7289e-001 -1.3979e+000 -1.3204e+0006.3633e-001 3.0354e-001 -2.2485e-002 1.5056e-0018.7955e-001 6.5016e-001 -8.0370e-002 2.1506e-001(2) C=A*B; D=(A*B); G=B*A; H=(B*A); C-Dans =-2.2376e-001 6.3633e-001 1.7227e-001 8.7955e-001-4.7289e-001 3.0354e-

15、001 1.1938e-001 6.5016e-001-1.3979e+000 -2.2485e-002 -2.9484e-001 -8.0370e-002-1.3204e+000 1.5056e-001 -2.3624e-001 2.1506e-001 C-G ans =-2.2376e-001 6.3633e-001 1.7227e-001 8.7955e-001-4.7289e-001 3.0354e-001 1.1938e-001 6.5016e-001 C-H ans =0000000000000000 D-G ans =0000000000000000 D-H ans =1.397

16、9e+000 2.2485e-002 2.9484e-001 8.0370e-002 1.3204e+000 -1.5056e-001 2.3624e-001 -2.1506e-001 G-Hans =2.2376e-001 -6.3633e-001 -1.7227e-001 -8.7955e-0014.7289e-001 -3.0354e-001 -1.1938e-001 -6.5016e-0011.3979e+000 2.2485e-002 2.9484e-001 8.0370e-0021.3204e+000 -1.5056e-001 2.3624e-001 -2.1506e-001 C=

17、inv(A*B); D=inv(A)*inv(B); G=inv(B*A); H=inv(B)*inv(A); C-Dans =-3.9602e+001 -1.4016e+001 1.4537e+001 2.2261e+001 1.5266e+001 1.5778e+001 -1.9398e+001 -3.9304e+0011.3845e+001 -5.5182e-001 2.6289e+001 5.1120e+001 C-G ans =-3.9602e+001 -1.4016e+001 1.4537e+001 2.2261e+0011.5266e+001 1.5778e+001 -1.939

18、8e+001 -3.9304e+0011.0821e+001 1.4313e+000 -2.7296e+001 -4.8956e+0011.3845e+001 -5.5182e-0012.6289e+0015.1120e+0011.3845e+001 -5.5182e-0012.6289e+0015.1120e+001 C-Hans =-5.6843e-014 -1.2879e-0143.0198e-0147.1054e-014-6.5370e-013 -1.4744e-0133.3396e-0138.2423e-013-1.5774e-012 -3.5527e-0137.8870e-0131

19、.9895e-012-5.6843e-014 -1.2879e-0143.0198e-0147.1054e-014-6.5370e-013 -1.4744e-0133.3396e-0138.2423e-013-1.5774e-012 -3.5527e-0137.8870e-0131.9895e-0121.8758e-0124.2988e-013 -9.4502e-013 -2.4016e-0121.8758e-012 D-G ans =4.9738e-013 1.1013e-013 -8.3489e-014 -3.1264e-0131.7053e-013 3.7303e-014 -2.4869

20、e-014 -1.0747e-0135.8265e-013 1.3145e-013 -9.4147e-014 -3.8369e-013-1.0516e-012 -2.3448e-013 1.7053e-013 6.6791e-013 D-H ans =3.9602e+001 1.4016e+001 -1.4537e+001 -2.2261e+001-1.5266e+001 -1.5778e+001 1.9398e+001 3.9304e+001-1.0821e+001 -1.4313e+000 2.7296e+001 4.8956e+001-1.3845e+001 5.5182e-001 -2

21、.6289e+001 -5.1120e+001 G-H ans =3.9602e+001 1.4016e+001 -1.4537e+001 -2.2261e+001-1.5266e+001 -1.5778e+001 1.9398e+001 3.9304e+001-1.0821e+001 -1.4313e+000 2.7296e+001 4.8956e+001-1.3845e+001 5.5182e-001 -2.6289e+001 -5.1120e+001(4) c=inv(A*B); d=inv(A*B); g=inv(A)*inv(B); h=(inv(A)*inv(B); c-dans

22、=-3.9602e+001 1.5266e+001 1.0821e+001 1.3845e+001-1.4016e+001 1.5778e+001 1.4313e+000 -5.5182e-0011.4537e+001 -1.9398e+001 -2.7296e+001 2.6289e+0012.2261e+001 -3.9304e+001 -4.8956e+001 5.1120e+001 c-gans =-1.6875e-014 -5.4712e-013 -1.3216e-012 1.5774e-012-2.8866e-015 -1.3145e-013 -3.1264e-013 3.7659

23、e-0138.8818e-015 2.6290e-013 6.3949e-013 -7.6028e-0132.5757e-014 7.1765e-013 1.7195e-012 -2.0606e-012 c-hans =-3.9602e+001 1.5266e+001 1.0821e+001 1.3845e+001-1.4016e+001 1.5778e+001 1.4313e+000 -5.5182e-0011.4537e+001 -1.9398e+001 -2.7296e+001 2.6289e+0012.2261e+001 -3.9304e+001 -4.8956e+001 5.1120

24、e+001 d-g ans =3.9602e+001 -1.5266e+001 -1.0821e+001 -1.3845e+0011.4016e+001 -1.5778e+001 -1.4313e+000 5.5182e-001-1.4537e+001 1.9398e+001 2.7296e+001 -2.6289e+001-2.2261e+001 3.9304e+001 4.8956e+001 -5.1120e+001 d-h ans =-2.4158e-013 -1.1724e-013 -2.7711e-013 5.2580e-013-5.6843e-014 -1.8652e-014 -5

25、.3291e-014 1.0658e-0134.2633e-0141.5987e-0131.7764e-0146.7502e-0144.7962e-014 -8.8818e-0141.8474e-013 -3.3396e-013 g-hans =-3.9602e+0011.5266e+0011.0821e+0011.3845e+001-1.4016e+0011.5778e+0011.4313e+000 -5.5182e-0011.4537e+001-1.9398e+001 -2.7296e+0012.6289e+0012.2261e+001-3.9304e+001 -4.8956e+0015.

26、1120e+001第二题：(1) n=200; A=floor(10*rand(n); b=sum(A); z=ones(n,1); c=linsolve(A,b); d=c-z ;精度为 1e-141e-13;tic,x=Ab,toc=Elapsed time is 0.016000 seconds.tic,x=Ab,toctic,inv(A)*b,toc=Elapsed time is 0.031000 seconds.tic,inv(A)*b,toc(2)n=500; tic,x=Ab;tocElapsed time is 0.187000 seconds. 更快！ tic,y=inv(

27、A)*b;tocElapsed time is 0.343000 seconds. max(abs(x-z)=4.3987e-013更精确! max(abs(y-z) = 2.2524e-012 n=1000; tic,x=Ab;tocElapsed time is 0.920000 seconds. 更快！ tic,y=inv(A)*b;tocElapsed time is 1.404000 seconds. max(abs(x-z) =1.8221e-012更精确! max(abs(y-z) =2.0862e-011(3) A=floor(10*rand(6);B=A ; A(:,6)=-

28、sum(B(1:5,:)A =06770-2058470-2467433-2385833-2718394-2573288-28 x=ones(6,1); b=A*xb =000000 det(A)= 0 rref(A)ans =10000-101000-100100-100010-100001-10000003.2 A=floor(10*rand(6); B=A; A(:,6)=-sum(B(1:5,:); B=x*1:6B =123456123456123456123456123456123456 A*Bans =0000000000000000000000000000000000003.3

29、 A=floor(10*rand(6); B=A; A(:,6)=-sum(B(1:5,:); C=floor(10*rand(6); B=x*1:6; D=B+C; A*C-A*D ans =0000000000000000000000000000000000004题： B=eye(10)-triu(ones(10),1); C=inv(B); B(10,1)=-1/256; B=eye(10)-triu(ones(10),1); B(10,1)=-1/256;行最简形： rref(B)ans =100000000-256010000000-128001000000-64000100000-

30、32000010000-16000001000-8000000100-4000000010-2000000001-10000000000 d=B*C;C =1124816326412825601124816326412800112481632640001124816320000112481600000112480000001124000000011200000000110000000001行最简形： rref(d)ans =10000000000100000000001000000000010000000000100000000001000000000010000000000100000000

31、00100000000000 det(B) ans =0 rref(B c) ans =100000000-2560010000000-1280001000000-640000100000-320000010000-160000001000-80000000100-40000000010-20000000001-1000000000001第五题：(1) A=floor(20*rand(6); B=floor(20*rand(6,1)-10; x=ABx =0.32683-2.76131.67640.76772-0.33957-1.5678 C=A B; a=rref(C)1000000.326

32、83010000-2.76130010001.67630001000.76772000010-0.33957000001-1.5678 a(:,7)-xans =1.3288e-0079.5485e-006-4.8037e-006-2.7883e-0065.0983e-007-1.9237e-006(2) A=floor(20*rand(6); B=floor(20*rand(6,1)-10; A(:,3)=A(:,1:2)*4 3; rref(A B)ans =104000001300000001000000010000000100000001 y=floor(20*rand(6,1)-10

33、; A=floor(20*rand(6); A(:,3)=A(:,1:2)*4 3; c=A*y184139197147292 rref(A c) ans =104000101300060001008000010-100000160000000 A=floor(20*rand(6); A(:,3)=A(:,1:2)*4 3; y=floor(20*rand(6,1)-10; c=A*y;10400023013000170001009000010000000170000000 w=23,17,0,9,0,7; A*w-cans =000000(5) A=floor(20*rand(6); A(:

34、,3)=A(:,1:2)*4 3; U=rref(A)104000013000000100000010000001000000 Z=-4,-3,1,0,0,0; A*Zans =000000(6) A=floor(20*rand(6);A(:,3)=A(:,1:2)*4 3; y=floor(20*rand(6,1)-10; c=A*y;104000001300000001000000010000000100000000 U=rref(A c)U =1 U=rref(A c)U =104000-23013000-220001004000010900000160000000 w=-23,-22,

35、0,4,9,6; v=w+3*z; A*v-c ans =00000第六题:(1)A=0,1,0,1,0,0,0,1;1,0,1,0,0,0,1,0;0,1,0,1,0,0,0,0;1,0,1,0,1,0,0,0;0,0,0,1,0,1,0,0;0,0,0,0,1,0,1,0;0,1,0,0,0,1,0,1;1,0,0,0,0,0,1,0A =0101000110100010010100001010100000010100000010100100010110000010 AA2 ans =30201020030201022020101002030101101020100101020120101

36、03002010102 A1=AA2+AA1 =331211312212112131011010110011011211221121001101101129015101129015109113010018010718017171151071101201sum(sum(A1(1:8,1:8)ans =72 A2=AA4+AA2 = TOC o 1-5 h z 18113111811513110111511590710908151100113010 sum(sum(A2(1:8,1:8) ans =A3 =1191861640103111191103064186861631470730110319

37、31560736404713815600640561381471031730561931186073047163 sum(sum(A3(1:8,1:8) ans =2362 A4=AA8+AA4 =79915771436069711799169704361577577141813160501016971614138105014360316124313810043603811243131669715010381161411577050103161418 sum(sum(A4(1:8,1:8)ans =15800(4) A5=AA3+AA5 =080703068060307006060203706

38、0504003050402302040500704050660302060 sum(sum(A5(1:8,1:8) ans =A6 =047041024034470340240410034031017023410310240330024024016017240170160240041033024031340230170310 sum(sum(A6(1:8,1:8) ans =922 A7=AA7+AA7 =03090270016702233090223016702700022301970120015927001970150023200167015009501201670120095015000

39、2700232015001972230159012001970 sum(sum(A7(1:8,1:8) ans =6098 AA2 ans =3020102003020102202010100203010110102010010102012010103002010102 AA4 ans =1801309015001801509013130100701000150150801090707080090807071501008015001301007010 AA6 ans =119086064010300119010306408686063047073001030930560736404703805

40、600640560380471030730560930086073047063 AA8ans =79905770436069700799069704360577577041803160501006970614038105014360316024303810043603810243031669705010381061400577050103160418 AA3ans =0706030570503060050502036050404003040302302030400604040550302050 AA5 ans =04604002403346033024040003303001702340030

41、0230330024023015017240170150230040033023030330230170300 AA7030802690167022230802220167026900222019601200159269019601490232001670149094012016701200940149002690232014901962220159012001960 B=A; B(3,6)=1; B(6,3)=1; B(5,8)=1; B(8,5)=1; BA2 ans =tvS 0L0L090LL0L090Z00L0L0L09L0L0L090090L0L0L90L0L0L00L090L0L

42、L090L0Z0=SUBCvS BA5 ans =061061610610061061610610060061600610061060610600060061600610061060610600061061610610061061610610ans =18301820182018200183018201820182182018301820182001820183018201821820182018301820018201820183018218201820182018300182018201820183 BA7 ans =054705470546054754705470546054700547

43、05470547054654705470547054600546054705470547546054705470547005470546054705475470546054705470 BA8 ans =16410164001640016400016410164001640016401640016410164001640001640016410164001640164001640016410164000164001640016410164016400164001640016410164001641(6) B(6,8)=1; B(8,6)=1; C=B; CC =0101000110100010

44、010101001010100000010101001010110100010110001110 CA2 ans =302021200302020220302021020302022020312112021412202021310 CA3 ans =21212140717161870706272170718167070726216172828628284871716282882628784ans =222202211121822122042242220222221821112202214224222142142313221311228221331132621421422132313822112

45、213261331 CA5 ans =1263156321702175638638643265321563126321752170638638653264322164216530793079703275327960796821652164307930797532703279687960第七题： A=magic(8)A =64236160675795554121351501617474620214342244026273736303133323435292838392541232244451918484915145253111056858595462631 c=1:8; b=rref(A c)1

46、0011001001034-3-470001-3-445-70000000001000000000000000000000000000000000000(2) A=magic(8)A =64236160675795554121351501617474620214342244026273736303133323435292838392541232244451918484915145253111056858595462631 b=8 -8 -8 8 8 -8 -8 8; U=rref(A b)U =10011001001034-3-47-8001-3-445-7800000000000000000

47、0000000000000000000000000000 x2=floor(10*rand(5,1)x2 =67 c=U(1:3,9); V=U(1:3,4:8); x1=-1*V*x2+cx1 =-14-6-10 x=x1;x2; A*x-bans =000第八题：B=-1,-1;1,1; A=zeros(2),eye(2);eye(2),BA =0010000110-1-10111 c=B*B TOC o 1-5 h z 0000 AA2 ans =10-1-10111-1-1101101 AA4 ans =10 -2-20122-2-2 102201 AA6 ans =10-3-3013

48、3-3-3103301 AA8ans =10-4-40144-4-4104401 symsk C=eye(2),k*B;k*B,eye AA(2*K)的通项C =1,。, -k，-k0, 1, k, k-k, -k, 1, 0 k, k, 0, 1 C*(AA2) ans =1,0, -k-1, -k-10,1, k+1, k+1 -k-1, -k-1,1,0k+1, k+1,0,1(2) AA3ans = TOC o 1-5 h z -1-1 10110110 -2-20122 AA5ans =-2-210220110-3-30133 AA7 ans =-3-310330110-4-4014

49、4 AA9 ans =-4-410440110-5-50155D=(k-1)/2*B,eye(2);eye(2),(k+1)/2*BAA(2k-1)的通项-1/2*k+1/2,-1/2*k+1/2,1,01/2*k-1/2, 1/2*k-1/2,0,11,0, -1/2*k-1/2, -1/2*k-1/20,1, 1/2*k+1/2, 1/2*k+1/2 D*AA2 ans =-1/2*k-1/2, -1/2*k-1/2,1,0 1/2*k+1/2, 1/2*k+1/2,0,11,0,-3/2-1/2*k, -3/2-1/2*k0,1, 3/2+1/2*k, 3/2+1/2*k D=(k+1)

50、/2*B,eye(2);eye(2),(k+3)/2*BD =-1/2*k-1/2, -1/2*k-1/2,1,0 1/2*k+1/2, 1/2*k+1/2,0,11,0, -3/2-1/2*k, -3/2-1/2*k1,0,1, 3/2+1/2*k, 3/2+1/2*k第九题： A=floor(10*rand(6)863143531682281383656865873887045563 Aans =852680638574311635163885488686323573 B=A*AB =19316591156188126165199100164222134911008110911880156

51、16410919921813518822211821828015612613480135156105 B11=B(1:3,1:3); B12=B(1:3,4:6); B21=B(4:6,1:3); B22=B(4:6,4:6); C=inv(B11); C1=C0.018496-0.012892-0.0048636-0.0128920.022223-0.012953-0.0048636-0.0129530.033801 G=B21*CG =0.240980.221640.801320.0413510.981470.198640.21390.317320.35559 H=B22-B21*C*B21H =37.71428.93610.83128.93630.93.381210.8313.38127.08 L=eye(3),zeros(3);G,eye(3)1000000100000010000.240980.221640.801321000.0413510.981470.198640100.21390.317320.35559001 D= B11,zeros(3);zeros(3),H1931659100016519910000091100810000037.71428.93610.83100028.93630.93.381200010.8313.38127.0