大连理工大学线性代数实验上机报告Word下载.docx
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大连理工大学线性代数实验上机报告Word下载.docx
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0.8035 1.06200.8347 1.14641.4334
计算A-B
A-B
ans=
0.0570 -0.6085-0.6658-0.2969 0.1660
0.16270.2467 0.27580.0402-0.4099
-0.2652 0.27000.6401 0.1502 0.2028
0.2579 0.9113-0.4648-0.0030 0.2246
0.4612 0.8678 0.7658 0.7726-0.0760
计算A*B+B*A
A*B+B*A
ans=
3.02882.3058 3.14392.72763.1034
2.90942.1967 3.0040 3.0737 3.2584
3.3422 2.1423 3.2104 3.57343.9049
4.1446 2.9794 4.3676 4.2354 4.9170
3.1350 1.7787 3.2289 3.11703.2815
求Ax=b的解
> x=A\b
x=
-0.9850
2.4396
3.3124
-5.6515
1.7085
验证克莱姆法则
c=A(:
1)
c=
0.8147
0.9058
0.1270
0.9134
0.6324
>d=A(:
2)
d=
0.0975
0.2785
0.5469
0.9575
0.9649
e=A(:
3)
e=
0.1576
0.9706
0.9572
0.4854
0.8003
f=A(:
4)
f =
0.1419
0.4218
0.9157
0.7922
0.9595
g=A(:
5)
g=
0.6557
0.0357
0.8491
0.9340
0.6787
B1=[b'
;
d'
;
e'
f'
g'
]'
B1=
0.2760 0.0975 0.1576 0.14190.6557
0.67970.2785 0.9706 0.4218 0.0357
0.6551 0.5469 0.95720.9157 0.8491
0.1626 0.9575 0.4854 0.7922 0.9340
0.1190 0.9649 0.8003 0.9595 0.6787
>B2=[c'
b'
e'
f';
]'
B2=
0.81470.2760 0.15760.1419 0.6557
0.90580.67970.97060.4218 0.0357
0.1270 0.6551 0.95720.91570.8491
0.91340.16260.4854 0.7922 0.9340
0.6324 0.1190 0.8003 0.95950.6787
B3=[c'
d'
B3 =
0.8147 0.09750.2760 0.14190.6557
0.90580.2785 0.6797 0.42180.0357
0.1270 0.54690.6551 0.9157 0.8491
0.9134 0.9575 0.1626 0.7922 0.9340
0.63240.9649 0.11900.9595 0.6787
B4=[c'
b'
B4 =
0.8147 0.0975 0.1576 0.2760 0.6557
0.9058 0.2785 0.9706 0.6797 0.0357
0.1270 0.54690.95720.65510.8491
0.91340.95750.4854 0.16260.9340
0.6324 0.96490.80030.1190 0.6787
B5=[c'
f'
b']'
B5=
0.81470.0975 0.15760.14190.2760
0.9058 0.27850.97060.42180.6797
0.1270 0.5469 0.9572 0.91570.6551
0.9134 0.9575 0.4854 0.7922 0.1626
0.63240.9649 0.80030.9595 0.1190
>x1=det(B1)/det(A)
x1=
-0.9850
>> x2=det(B2)/det(A)
x2=
2.4396
x3=det(B3)/det(A)
x3=
3.3124
> x4=det(B4)/det(A)
x4=
-5.6515
x5=det(B5)/det(A)
x5=
1.7085
计算A的行列式
det(A)
-0.0250
计算B的行列式
det(B)
ans =
0.0647
求A的逆
inv(A)
ans=
3.1375 -0.8078-1.8788-4.2194 5.1680
-8.6076 3.5314 2.890713.7204-14.3665
-6.2824 3.72203.6132 10.0084 -12.4190
13.6173-6.8822 -6.3938 -23.5288 27.5825
-2.5292 1.0729 2.4193 5.8870-7.2671
求B的逆
inv(B)
-0.4430 3.4997 1.3255-2.6005 -0.4697
1.4047-1.16260.2422-0.4475 -0.0119
0.7210 -1.8189 -2.0635 2.44340.0765
-0.6122 -0.1837 2.0165 0.0375-1.2564
0.0384 -0.5157 -0.7370 0.5267 1.7407
求A的秩
>>rank(A)
5
求B的秩
rank(B)
ans=
5
求A*B的行列式
det(A*B)
ans =
-0.0016
求A*B的逆
inv(A*B)
-74.0649 35.0433 31.2288 121.5740-137.3442
6.8291 -1.2718 -2.2922 -8.9951 8.6972
63.9620-31.4202 -29.5061 -105.6918 122.3246
-9.3196 5.7452 4.6259 11.9660-15.4028
11.9582 -6.3521 -3.3817-16.7574 18.6360
rank(A*B)
ans =
>det(A)*det(B)
-0.0016
验证
(1)
(A*B)'
0.9569 1.5566 1.6237 2.2732 2.2552
0.69220.9401 0.4969 0.93710.8090
0.94611.64921.6875 2.3563 2.3800
0.7507 1.5887 1.8840 1.9421 2.1481
1.1399 1.52122.2149 2.45452.4497
B'
*A'
0.9569 1.55661.6237 2.27322.2552
0.69220.94010.49690.9371 0.8090
0.9461 1.6492 1.6875 2.35632.3800
0.75071.5887 1.8840 1.9421 2.1481
1.13991.5212 2.2149 2.45452.4497
(2)
inv(B)*inv(A)
ans=
-74.064935.0433 31.2288 121.5740-137.3442
6.8291 -1.2718 -2.2922 -8.99518.6972
63.9620-31.4202 -29.5061-105.6918 122.3246
-9.3196 5.7452 4.6259 11.9660-15.4028
11.9582 -6.3521-3.3817-16.757418.6360
(3)
A*B
0.95690.6922 0.9461 0.7507 1.1399
1.55660.9401 1.6492 1.58871.5212
1.62370.4969 1.6875 1.8840 2.2149
2.2732 0.9371 2.3563 1.9421 2.4545
2.25520.8090 2.3800 2.14812.4497
B*A
2.07191.61352.19781.9769 1.9635
1.3528 1.2566 1.3549 1.4850 1.7372
1.7186 1.6454 1.52291.6894 1.6900
1.8714 2.0423 2.0113 2.2932 2.4625
0.8797 0.9697 0.8489 0.9690 0.8317
求矩阵X使得AXB=C
首先随机生成五阶方阵C
>C=rand(5)
C =
0.49840.75130.9593 0.8407 0.3500
0.9597 0.2551 0.5472 0.25430.1966
0.34040.5060 0.1386 0.8143 0.2511
0.5853 0.6991 0.1493 0.2435 0.6160
0.2238 0.8909 0.2575 0.9293 0.4733
X=A的逆*B的逆
>X=inv(A)*C*inv(B)
X=
3.8432 -13.8858 2.1418 9.4404 -4.5871
-9.331241.9602-7.9101-28.4683 14.8942
-7.8738 35.1218 -5.4107-22.886110.1581
16.7545-75.6079 14.6784 49.3951-24.7450
-3.5568 17.0848 -2.9018 -11.2670 5.4559
实验二
1.验证:
对于一般的方阵A,B,C,D,
首先随机生成方阵A,B,C,D
A=rand(5)
A =
0.82580.10670.8687 0.43140.1361
0.5383 0.9619 0.0844 0.9106 0.8693
0.9961 0.0046 0.39980.1818 0.5797
0.0782 0.7749 0.2599 0.2638 0.5499
0.4427 0.8173 0.8001 0.1455 0.1450
>>B=rand(5)
B=
0.85300.0760 0.4173 0.4893 0.7803
0.6221 0.2399 0.0497 0.3377 0.3897
0.3510 0.1233 0.90270.9001 0.2417
0.5132 0.1839 0.9448 0.3692 0.4039
0.40180.2400 0.4909 0.1112 0.0965
C=rand(5)
C=
0.13200.2348 0.1690 0.54700.1835
0.94210.35320.6491 0.29630.3685
0.9561 0.8212 0.73170.7447 0.6256
0.57520.0154 0.6477 0.1890 0.7802
0.05980.0430 0.4509 0.68680.0811
D=rand(5)
D=
0.92940.3063 0.6443 0.9390 0.2077
0.7757 0.50850.3786 0.87590.3012
0.48680.51080.8116 0.5502 0.4709
0.4359 0.8176 0.5328 0.6225 0.2305
0.4468 0.7948 0.35070.5870 0.8443
>Z=[A,B;
C,D]
Z=
0.82580.1067 0.86870.4314 0.1361
0.8530ﻩﻩ0.0760 0.4173 0.4893 0.7803
0.5383 0.9619 0.0844 0.91060.8693
0.6221 0.2399 0.04970.3377 0.3897
0.99610.0046 0.3998 0.18180.5797
0.3510 0.1233 0.9027 0.90010.2417
0.0782 0.7749 0.25990.2638 0.5499
0.51320.18390.9448 0.36920.4039
0.4427 0.81730.80010.1455 0.1450 0.40180.24000.4909 0.1112 0.0965
0.1320 0.23480.1690 0.5470 0.1835 0.92940.3063 0.6443 0.9390 0.2077
0.9421 0.3532 0.6491 0.29630.36850.7757 0.5085 0.3786 0.8759 0.3012
0.9561 0.8212 0.7317 0.7447 0.6256 0.4868 0.5108 0.8116 0.5502 0.4709
0.5752 0.0154 0.6477 0.18900.7802 0.4359 0.8176 0.53280.62250.2305
0.0598 0.0430 0.4509 0.6868 0.0811 0.44680.79480.3507 0.5870 0.8443
求Z的行列式
det(Z)
ans=
-0.0295
求det(A)*det(D)-det(B)*det(C)
det(A)*det(D)-det(B)*det(C)
ans =
1.8656e-004
随机生成对角矩阵A
A=diag([randrandrandrand rand])
0.1948 0 0 0 0
00.2259 0 0 0
0 0 0.1707 0 0
0 0 0 0.2277 0
00 0 0 0.4357
随机生成对角矩阵B
B=diag([randrandrand randrand])
0.3111 00 0 0
0 0.9234 0 0 0
0 00.4302 0 0
00 00.1848 0
0 0 0 0 0.9049
随机生成对角矩阵C
C=diag([randrandrandrandrand])
C=
0.9797 0 0 0 0
0 0.4389 0 0 0
0 0 0.1111 0 0
0 0 00.2581 0
0 0 0 0 0.4087
随机生成对角矩阵D
> D=diag([rand randrandrand rand])
D =
0.5949 0 0 0 0
0 0.2622 0 0 0
0 0 0.6028 0 0
0 0 0 0.7112 0
0 0 0 0 0.2217
> Z=[A,B;
C,D]
Z =
0.1948 0 0 000.3111 0 0 0 0
0 ﻩﻩ0.2259 0 0 0
0 0.9234 0 0 0
0ﻩ00.1707 0 0 00 ﻩ0.4302 0 0
0 0 0 ﻩ0.2277 0
0 0 0 0.18480
0 0 0 0 0.4357 0 ﻩ0 00 0.9049
0.9797 0 0 0 0 0.5949 0 0 0 0
00.4389 0 0 0 0 0.2622 0 00
0 0 0.1111 0 0 0 0 0.6028 00
0 0 00.25810 0 0 0 0.7112 0
0 0 0 0 0.4087 0 0 0 0 0.2217
计算Z的行列式
det(Z)
-1.1243e-004
计算det(A)*det(D)-det(B)*det(C)
det(A)*det(D)-det(B)*det(C)
-9.3107e-005
计算A*D-B*C的行列式
det(A*D-B*C)
-1.1243e-004
实验三
求A列向量组的一个最大无关组,并把不属于
极大无关组的向量利用极大无关组表示.
N= 200865083;
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];
> B=rref(A)
B
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