大连理工大学线性代数实验上机报告材料

1、实用标准文档大连理工大学线性代数实验上机报告实验一首先随机生成五阶方阵AA=rand(5)A =0.81470.09750.15760.14190.65570.90580.27850.97060.42180.03570.12700.54690.95720.91570.84910.91340.95750.48540.79220.93400.63240.96490.80030.95950.6787>> B=rand(5)随机生成五阶方阵BB =0.75770.70600.82350.43870.48980.74310.03180.69480.38160.44560.39220.2769

2、0.31710.76550.64630.65550.04620.95020.79520.70940.17120.09710.03440.18690.7547>> b=rand(1,5)'随机生成列向量bb =0.27600.67970.65510.16260.1190计算 A+B>> A+Bans =1.57251.64890.51921.56890.80350.80360.31030.82381.00371.06200.98111.66541.27431.43560.83470.58060.80331.68131.58741.14641.14550.48131

3、.49541.64341.4334计算 A-B >> A-Bans =0.0570-0.6085-0.6658-0.29690.16600.16270.24670.27580.0402-0.4099-0.26520.27000.64010.15020.20280.25790.9113-0.4648-0.00300.22460.46120.86780.76580.7726-0.0760计算 A*B+B*A>> A*B+B*Aans =3.02882.30583.14392.72763.10342.90942.19673.00403.07373.25843.34222.14

4、233.21043.57343.90494.14462.97944.36764.23544.91703.13501.77873.22893.11703.2815求 Ax=b 的解>> x=Abx =-0.98502.43963.3124-5.65151.7085验证克莱姆法则>> c=A(:,1)c =0.81470.90580.12700.91340.6324>> d=A(:,2)d =0.09750.27850.54690.95750.9649>> e=A(:,3) e =0.15760.97060.95720.48540.8003>&

5、gt; f=A(:,4)f =0.14190.42180.91570.79220.9595>> g=A(:,5)g =0.65570.03570.84910.93400.6787>> B1=b'd'e'f'g''B1 =0.27600.67970.65510.16260.11900.09750.27850.54690.95750.96490.15760.97060.95720.48540.80030.14190.42180.91570.79220.95950.65570.03570.84910.93400.6787>

6、> B2=c'b'e'f'g''B2 =0.81470.90580.12700.91340.63240.27600.67970.65510.16260.11900.15760.97060.95720.48540.80030.14190.42180.91570.79220.95950.65570.03570.84910.93400.6787文案大全>> B3=c'd'b'f'g''B3 =0.81470.90580.12700.91340.63240.09750.27850.5469

7、0.95750.96490.27600.67970.65510.16260.11900.14190.42180.91570.79220.95950.65570.03570.84910.93400.6787>> B4=c'd'e'b'g''0.65570.03570.84910.93400.67870.27600.67970.65510.16260.1190B4 =0.8147 0.0975 0.1576 0.27600.9058 0.2785 0.9706 0.67970.1270 0.5469 0.9572 0.65510.9134

8、 0.9575 0.4854 0.16260.6324 0.9649 0.8003 0.1190>> B5=c'd'e'f'b''B5 =0.8147 0.0975 0.1576 0.14190.9058 0.2785 0.9706 0.42180.1270 0.5469 0.9572 0.91570.9134 0.9575 0.4854 0.79220.6324 0.9649 0.8003 0.9595>> x1=det(B1)/det(A)x1 =-0.9850>> x2=det(B2)/det(A) x2

9、 =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)ans =-0.0250计算 B 的行列式>> det(B)ans =0.0647求 A 的逆>> inv(A)5.1680ans =3.1375 -0.8078 -1.8788 -4.2194-8.6076 3.5314 2.8907 13.7204-6.2824 3.7220 3.613

10、2 10.008413.6173 -6.8822 -6.3938 -23.5288-2.5292 1.0729 2.4193 5.8870求 B 的逆>> inv(B)ans =-0.4430 3.4997 1.3255 -2.60051.4047 -1.1626 0.2422 -0.44750.7210 -1.8189 -2.0635 2.4434-0.6122 -0.1837 2.0165 0.03750.0384 -0.5157 -0.7370 0.5267求 A 的秩>> rank(A)ans =5求 B 的秩-14.3665-12.419027.5825-7.

11、2671-0.4697-0.01190.0765-1.25641.7407>> 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)ans =-74.0649 35.0433 31.2288 121.5740 -137.34426.8291 -1.2718 -2.2922 -8.9951 8.697263.9620 -31.4202 -29.5061 -105.6918 122.3246-9.3196 5.7452 4.6259 11.9660 -15.402811.9582 -6

12、.3521 -3.3817 -16.7574 18.6360>> rank(A*B)实用标准文档ans =5>> det(A)*det(B)ans =-0.0016验证(AB? =BTAT,(ABf1=B'AAB#BA(1)>> (A*B)'ans =0.95690.69220.94610.75071.13991.55660.94011.64921.58871.52121.62370.49691.68751.88402.21492.27320.93712.35631.94212.45452.25520.80902.38002.14812.44

13、97>> B'*A'ans =0.95690.69220.94610.75071.13991.55660.94011.64921.58871.52121.62370.49691.68751.88402.21492.27320.93712.35631.94212.45452.25520.80902.38002.14812.44972) >> inv(B)*inv(A) ans =-74.0649 35.0433 31.2288 121.5740 -137.34426.8291 -1.2718 -2.2922 -8.9951 8.697263.9620 -3

14、1.4202 -29.5061 -105.6918 122.3246-9.3196 5.7452 4.6259 11.9660 -15.402811.9582 -6.3521 -3.3817 -16.7574 18.6360( 3)>> A*Bans =0.9569 0.6922 0.9461 0.75071.5566 0.9401 1.6492 1.58871.6237 0.4969 1.6875 1.88402.2732 0.9371 2.3563 1.94212.2552 0.8090 2.3800 2.1481>> B*Aans =2.0719 1.6135 2

15、.1978 1.97691.3528 1.2566 1.3549 1.48501.7186 1.6454 1.5229 1.68941.8714 2.0423 2.0113 2.29320.8797 0.9697 0.8489 0.9690求矩阵X 使得AXB=C首先随机生成五阶方阵C>> C=rand(5)1.13991.52122.21492.45452.44971.96351.73721.69002.46250.8317C =文案大全实用标准文档0.49840.95970.34040.58530.22380.75130.25510.50600.69910.89090.9593

16、0.54720.13860.14930.25750.84070.25430.81430.24350.92930.35000.19660.25110.61600.4733X=A的逆*B的逆>> X=inv(A)*C*inv(B)3.8432 -13.8858 2.1418 9.4404 -4.5871-9.331241.9602-7.9101-28.468314.8942-7.873835.1218-5.4107-22.886110.158116.7545-75.607914.6784 49.3951-24.7450-3.556817.0848-2.9018-11.26705.455

17、9实验二1 .验证：对于一般的方阵A,B,C,D ,#|a d - b|c首先随机生成方阵A,B,C,DA=rand(5)0.82580.10670.86870.43140.13610.53830.96190.08440.91060.86930.99610.00460.39980.18180.57970.07820.77490.25990.26380.54990.44270.81730.80010.14550.1450>> B=rand(5)B =0.85300.07600.41730.48930.78030.62210.23990.04970.33770.38970.35100.

18、12330.90270.90010.24170.51320.18390.94480.36920.40390.40180.24000.49090.11120.0965>> C=rand(5)文案大全0.18350.36850.62560.78020.08110.20770.30120.47090.23050.84430.1320 0.2348 0.1690 0.54700.9421 0.3532 0.6491 0.29630.9561 0.8212 0.7317 0.74470.5752 0.0154 0.6477 0.18900.0598 0.0430 0.4509 0.6868&

19、gt;> D=rand(5)D =0.9294 0.3063 0.6443 0.93900.7757 0.5085 0.3786 0.87590.4868 0.5108 0.8116 0.55020.4359 0.8176 0.5328 0.62250.4468 0.7948 0.3507 0.5870>> Z=A,B;C,DZ =0.8258 0.1067 0.8687 0.4314 0.13610.85300.07600.41730.48930.78030.53830.96190.08440.91060.86930.62210.23990.04970.33770.3897

20、0.99610.00460.39980.18180.57970.35100.12330.90270.90010.24170.07820.77490.25990.26380.54990.51320.18390.94480.36920.40390.44270.81730.80010.14550.14500.40180.24000.49090.11120.09650.13200.23480.16900.54700.18350.92940.30630.64430.93900.20770.94210.35320.64910.29630.36850.77570.50850.37860.87590.3012

21、0.95610.82120.73170.74470.62560.48680.51080.81160.55020.47090.57520.01540.64770.18900.78020.43590.81760.53280.62250.23050.05980.04300.45090.68680.08110.44680.79480.35070.58700.8443求 Z 的行列式>> det(Z)实用标准文档ans =-0.0295求 det(A)*det(D)-det(B)*det(C)>> det(A)*det(D)-det(B)*det(C)ans =1.8656e-0

22、04随机生成对角矩阵A> > A=diag(rand rand rand rand rand)A =0.194800000 0.225900000 0.170700000 0.227700000 0.4357随机生成对角矩阵B> > B=diag(rand rand rand rand rand)B =0.311100000 0.923400000 0.430200000 0.184800000 0.9049随机生成对角矩阵C> > C=diag(rand rand rand rand rand)C =0.979700000 0.438900000 0.11

23、1100000 0.258100000 0.4087随机生成对角矩阵D> > D=diag(rand rand rand rand rand)D =0.594900000 0.262200000 0.602800000 0.711200000 0.2217>> Z=A,B;C,DZ =文案大全0.19480000.311100000.2259000.92340000000000000000000.97970000000000.1707000.4302000.227700.184800.435700.904900.59490.43890.26220.11110.60280

24、.2581 0.71120 0.4087 0 0.2217计算 Z 的行列式>> det(Z) ans =-1.1243e-004计算 det(A)*det(D)-det(B)*det(C) >> det(A)*det(D)-det(B)*det(C) ans =-9.3107e-005计算 A*D-B*C 的行列式>> det(A*D-B*C) ans =-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=8

25、3;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)1.0000000 -0.35480.46560 1.000000 -1.4905-2.002000 1.00000 0.04730.3950000 1.0000 1.79841.3383所以 a1,a2,a3,a4 是一个极大无关组。a5=-0,3548a1-1.4905a2+0.0473a3+1.7984a4;a6=0.4656a1-2.0020a2+0.3950a3+1.3383a4.实验四> > a=

26、83;> > b=86;> > c=50;> > d=88;> > e=28;> > f=63;> > g=83;> > h=60;> > b1=1,1.9,f,c;b2=1,1.8,f,c;A1=a,b,c,d;0.5,1,1.5,2;12,15,22,17;e,f,g,h;A2=a,b,c,d;0.3,0.6,0.9,1.2;12,15,22,17;e,f,g,h;A3=a,b,c,d;0.1,0.2,0.3,0.4;12,15,22,17;e,f,g,h;A4=a,b,c,d;0.05,0.1

27、,0.15,0.2;12,15,22,17;e,f,g,h;>> x1=A1/b1x1 =1.20430.03040.35171.2940>> x2=A2/b1x2 =1.20430.0182实用标准文档0.35171.2940>> x3=A3/b1x3 =1.20430.00610.35171.2940>> x4=A4/b1x4 =1.20430.00300.35171.2940>> x5=A2/b1x5 =1.20430.01820.35171.2940>> x6=A2/b2x6 =1.20310.01820.3514

28、1.2931>> x5=A1/b2x5 =0.03040.35141.2931>> x6=A2/b2x6 =1.20310.01820.35141.2931>> x7=A3/b2x7 =1.20310.00610.35141.2931文案大全实用标准文档>> x8=A4/b2 x8 =1.20310.00300.35141.2931实验五随机生成4 个 5 维向量，并进行正交化随机生成4 个 5 维向量a=rand(4,5);>> a0.11740.29670.31880.42420.50790.08550.26250.80100.0

29、2920.92890.73030.48860.57850.23730.45880.96310.54680.52110.23160.4889正交化>> b=null(a)b =0.6777-0.5941-0.30090.28920.1163实验六随机生成 5 阶矩阵 ，求其特征值及对应特征向量eig(A)ans =3.20370.5684-0.1026 + 0.5388i-0.1026 - 0.5388i-0.0457>> d,v=eig(A)文案大全实用标准文档0.2283-0.53540.0179 + 0.1710i0.0179 - 0.1710i-0.13830.3

30、2430.14990.70770.70770.46290.51410.7181-0.1450 + 0.3831i-0.1450 - 0.3831i0.31060.5300-0.4077-0.3302 - 0.3239i-0.3302 + 0.3239i-0.79140.54550.0944-0.1645 - 0.2465i-0.1645 + 0.2465i0.2091d 的每一列即为一个特征向量3.2037000000.568400000-0.1026 +0.5388i00000-0.1026 - 0.5388i00000-0.0457V中非零值即为每一列特征向量对应的特征值随机生成 5 维列向量 x第一组>> X=rand(1,5)'0.60200.26300.68920.7482求 X*X'>> X*X'ans =0.45040.19670.48940.51560.55970.3624 0.1583 0.3937 0.41490.1