matlab上机习题3Word下载.docx
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matlab上机习题3Word下载.docx
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(元素单位为度),其中A如第1题。
8.计算复数矩阵C每个元素的模、相角和共轭。
9.分别使用函数fix()、floor()、ceil()和
round(),计算第8题中的相角结果。
10.将2-i的模结果近似为有理数,并以数值形式
显示。
11.计算,其中m
=
4!
和n是42与35的最大公因数。
12.将球坐标系中的点(1,1,1)分别转换到笛卡尔
坐标系和极坐标系。
答案:
(1)
17241850
23571449
46132043
1012192162
111825256
>
norm(A)
ans=
131.0107
det(A)
0
rank(A)
4
null(A)
-0.4472
0.4472
orth(A)
-0.4263-0.74880.07630.4998
-0.4175-0.16890.5486-0.6999
-0.36680.50300.22280.3480
-0.52910.39710.07440.1958
-0.4790-0.0102-0.7988-0.3176
范数:
131.0107
行列式:
:
秩:
4
化零空间
正交空间:
-0.4263-0.74880.07630.4998
(2)ans=
1.0e+013*
-9.6231
9.6231
(3)LU分解
L1=
Columns1through4
0.73911.000000
1.0000000
0.17390.25270.51641.0000
0.43480.48390.72310.9231
0.47830.76871.00000
Column5
1.0000
U1=
23.00005.00007.000014.0000
020.3043-4.1739-2.3478
0024.8608-2.8908
00019.6512
0000
49.0000
13.7826
21.9700
19.6512
-0.0000
Schur分解:
U=
0.42770.6847-0.4495-0.37980.0441
0.42320.33120.83400.09600.0800
0.3756-0.5054-0.0074-0.40210.6646
0.5335-0.4029-0.0203-0.1850-0.7200
0.4607-0.0614-0.31920.80660.1774
L=
105.4509-4.4814-26.740868.934523.4299
021.48272.13733.0889-0.9642
00-13.8344-5.0667-7.8447
000-1.099216.9608
0000-0.0000
(4)QR分解
Q=
-0.55630.67950.4725-0.0753
-0.7526-0.65450.0465-0.0550
-0.13090.1801-0.5421-0.8103
-0.32720.2784-0.69330.5786
R=
-30.5614-21.8249-13.7428-24.4753-90.6044
017.45493.72765.719226.9017
00-19.4227-20.9714-40.3941
000-5.4266-5.4266
奇异值分解
-0.4845-0.7502-0.4288-0.1361
-0.4786-0.17480.8595-0.0410
-0.41900.5001-0.1668-0.7392
-0.60060.3956-0.22260.6583
S=
115.35670000
021.9825000
0013.653200
0003.63130
V=
-0.2334-0.49210.70210.1019-0.4472
-0.2058-0.5064-0.7079-0.0021-0.4472
-0.17940.5479-0.05930.6813-0.4472
-0.27370.44850.0434-0.7225-0.4472
-0.8922-0.0022-0.02180.05850.4472
(5)A=
0.42770.70650.3859-0.44830.4472
0.42320.3533-0.8848-0.44560.4472
0.3756-0.4846-0.1039-0.47960.4472
0.5335-0.3739-0.1193-0.40850.4472
0.4607-0.03670.20790.4511-0.4472
D=
105.45090000
021.4827000
00-13.834400
000-1.09920
00000.0000
不可对角化
(6)
expm(A)
1.0e+045*
0.69220.82590.99030.50853.0169
0.68490.81710.97980.50312.9848
0.60790.72530.86970.44652.6495
0.86341.03011.23520.63423.7629
0.74550.88951.06660.54763.2492
sqrtm(A)
3.1422+1.5354i2.6527-0.5898i-0.1313+6.7619i-0.6377-6.5360i5.0259+1.1715i
2.1267-1.3643i1.9892+3.6667i0.7289+6.1658i0.0890-7.2275i4.9338+1.2407i
-0.3799+0.4650i0.2987+1.1016i2.6301+7.0072i1.7416-7.2895i4.2904+1.2843i
0.3536+0.3258i1.0020+1.0417i2.9542+5.9550i1.8186-6.2267i6.1285+1.0958i
1.1181-0.1864i1.3910-1.4056i1.8402-6.5432i0.9745+6.9205i
Funm(A,@cos)
-0.4064-0.7520-2.87964.0061-1.0319
-0.4514-0.2902-3.10723.8264-1.0225
0.1589-0.1898-3.25933.3098-0.9804
0.0601-0.2623-3.64893.8231-1.0281
0.20180.41493.2638-3.66271.2178
(7)指数
1.0e+026*
0.00000.00000.00000.00000.0001
0.00000.00000.00000.00000.0000
0.00000.00000.00000.00008.4384
0.00000.00000.00000.00000.0209
余弦
-0.27520.42420.5403-0.14550.9650
-0.53280.28370.75390.13670.3006
-0.65360.96020.90740.40810.5551
-0.83910.84390.9887-0.54770.6735
0.00440.66030.9912-0.41610.8532
开平方
4.12314.89901.00002.82847.0711
4.79582.23612.64583.74177.0000
2.00002.44953.60564.47216.5574
3.16233.46414.35894.58267.8740
3.31664.24265.00001.41427.4833
(8)模5.00002.23611.0000
2.00002.00000
相角
0.9273-0.4636-1.5708
03.14160
共轭
3.0000-4.0000i2.0000+1.0000i0+1.0000i
2.0000-2.00000
(9)fix()
3.0000+4.0000i2.0000-1.0000i0-1.0000i
floor()
ceil()
2.0000-2.00000
round()
(10)
eval(rat(abs(2-i)))
2.2361
(11)
factorial(4)
24
gcd(42,35)
ans=7
nchoosek(24,7)
346104
(12)[THETA,PHI,R]=sph2cart(1,1,1);
P=[THETA,PHI,R]
P=
0.29190.45460.8415
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