线性代数上机实验报告Word下载.docx
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线性代数上机实验报告Word下载.docx
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57121514
149131414
81071113
A-B
0-5-6-32
1331-4
-33612
29-502
4877-1
2.
A*B+B*A
238182235208240
240166238244260
281174255293322
336232342333390
279142266258268
3.
x=A\b
x=
0.1142
0.8656
0.2325
-0.9006
0.3339
c=zeros(5,1);
c
c=
0
fori=1:
5
A0=A
A0(:
i)=b;
c(i)=det(A0)/det(A);
end
A0=
0.3339
因为c=x,所以克莱姆法则得证。
4.
det(A)
-4448
A^-1
0.16280.0063-0.1124-0.16550.2077
-0.43570.14610.10480.7302-0.6776
-0.21990.18210.17670.3561-0.4906
0.4960-0.2819-0.2513-1.01801.1965
0.0034-0.01510.12610.1817-0.2471
r=rank(A);
r
r=
5
det(B)
4568
B^-1
-0.03280.32090.1401-0.2351-0.0832
0.1655-0.1375-0.0061-0.03500.0193
0.0661-0.1528-0.21540.23340.0342
-0.0591-0.02230.2522-0.0232-0.1497
0.0026-0.0657-0.11120.07880.2067
rank(B)
5.
A*B
7850675786
13766137132122
14232136154182
19364185152190
19956198175198
det(A*B)
-2.0318e+07
(A*B)^-1
-0.29290.13970.11070.5139-0.5538
0.0709-0.0106-0.0229-0.09080.0839
0.2406-0.1274-0.1159-0.43060.4937
-0.06740.05110.03580.0797-0.1116
0.0933-0.0552-0.0206-0.13070.1428
r=rank(A*B)
det(A)*det(B)
-20318464
所以相等。
6.
(A*B)'
78137142193199
5066326456
67137136185198
57132154152175
86122182190198
B'
*A'
B^-1*A^-1
B*A
160132168151154
103100101112138
139142119139140
143168157181200
8086688370
7.
X=A^-1*C*B^-1
X=
-0.0065-0.4315-0.10330.46700.2040
0.32470.92500.5661-1.4216-0.8980
0.23720.79230.6485-1.1599-0.6314
-0.4807-1.5785-1.32902.43761.5380
0.08540.19630.1608-0.2801-0.1636
(二)
A=round(9*rand(3,3))
357
787
533
B=round(9*rand(3,3))
551
175
084
C=round(9*rand(3,3))
071
335
152
D=round(9*rand(3,3))
D=
648
611
727
det([A,B;
C,D])
7.2510e+03
det(A)*det(D)-det(B)*det(C)
4.1400e+03
A=diag(round(9*rand(1,3)))
500
090
001
C=diag(round(9*rand(1,3)))
400
010
009
-131844
det(A*D-C*B)
-1.3184e+05
得证。
(三)
a=83;
b=86;
c=50;
d=88;
e=28;
f=63;
g=83;
h=60;
A=[a,b,c,d,3,4;
1,2,3,4,4,3;
12,15,22,17,5,7;
e,f,g,h,8,0]
8386508834
123443
1215221757
2863836080
B=rref(A)
1.0000000-0.35480.4656
01.000000-1.4905-2.0020
001.000000.04730.3950
0001.00001.79841.3383
(四)
alpha=[-0.1,-0.2]
alpha=
-0.1000-0.2000
beta=[-0.5,-0.7,-0.9,-0.95]
beta=
-0.5000-0.7000-0.9000-0.9500
2
forj=1:
4
B=[1;
2+alpha(i);
f;
c];
A=[a,b,c,d;
1+beta(j),2+2*beta(j),3+3*beta(j),4+4*beta(j);
12,15,22,17;
e,f,g,h];
x=A\B
7.2103
-10.1055
6.1249
-0.3935
6.6667
-10.7424
5.8640
0.8899
3.9485
-13.9265
4.5591
7.3068
-0.1288
-18.7028
2.6017
16.9323
7.2533
-10.0553
6.1455
-0.4949
6.7382
-10.6586
5.8983
0.7210
4.1631
-13.6752
4.6621
6.8002
0.3004
-18.2000
2.8078
15.9191
(五)
A=round(9*rand(5,1))
7
8
1
B=round(9*rand(5,1))
C=round(9*rand(5,1))
D=round(9*rand(5,1))
a=orth([A,B,C,D])
a=
-0.27820.3020-0.2568-0.6726
-0.4033-0.3536-0.23670.5740
-0.4132-0.27310.8409-0.1995
-0.5499-0.4066-0.4058-0.2571
-0.53560.73750.07940.3350
(六)
88297
93450
41110
47122
34836
lambda=eig(A)
lambda=
22.0895+0.0000i
3.2998+0.0000i
-1.2872+3.8777i
-1.2872-3.8777i
-2.8148+0.0000i
[d,v]=eig(A)
d=
0.6992+0.0000i-0.1921+0.0000i0.5452+0.0000i0.5452+0.0000i-0.3311+0.0000i
0.4560+0.0000i0.4096+0.0000i-0.3336-0.3599i-0.3336+0.3599i-0.3474+0.0000i
0.1706+0.0000i0.0037+0.0000i-0.1931-0.2950i-0.1931+0.2950i0.2229+0.0000i
0.3457+0.0000i0.3674+0.0000i-0.2617+0.2859i-0.2617-0.2859i0.8217+0.0000i
0.3930+0.0000i-0.8126+0.0000i0.0495+0.4301i0.0495-0.4301i-0.2116+0.0000i
v=
22.0895+0.0000i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i
0.0000+0.0000i3.2998+0.0000i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i
0.0000+0.0000i0.0000+0.0000i-1.2872+3.8777i0.0000+0.0000i0.0000+0.0000i
0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i-1.2872-3.8777i0.0000+0.0000i
0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i0.0000+0.0000i-2.8148+0.0000i
x=round(9*rand(5,1))
x*x'
4942283521
4236243018
2824162012
3530202515
211812159
lambda=eig(x*x'
)
-0.0000
0.0000
135.0000
(七)
A=[1,3/2,0;
3/2,-1,1;
0,1,1]
1.00001.50000
1.5000-1.00001.0000
01.00001.0000
[P,D]=schur(A)
P=
-0.4222-0.55470.7170
0.8617-0.00000.5074
-0.28150.83210.4780
-2.061600
01.00000
002.0616
非正定
B=[1,0,2;
0,-1,-2;
2,-2,0]
102
0-1-2
2-20
[P,D]=schur(B)
-0.33330.6667-0.6667
0.66670.66670.3333
0.6667-0.3333-0.6667
-3.000000
00.00000
003.0000
(八)
A=[15,9,6]
1596
b=[15,9,6]
B=[0.7,0.2,0.1;
0.2,0.7,0.1;
0.1,0.1,0.8]
0.70000.20000.1000
0.20000.70000.1000
0.10000.10000.8000
C=A*B
12.90009.90007.2000
C1=A*B
C1=
C2=C1*B
C2=
11.730010.23008.0400
100年后,各行业人数如下计算
C100=A*B;
99
C100=C100*B;
C100
C100=
10.000010.000010.0000
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