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Розширення: docx
Розмір: 29кб.
Дата: 22.05.2020
скачати
Пов'язані файли:
kursova.doc
>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
(5==10)&(7>1)
ans =
1
>> %%----------------------
>>
>> % Завдання: логічні оператори
>>
(5==10)&(7>1)
ans =
1
>> (4==5)|(1
=2)
ans =
1
>> (4>=5)|(2
=2)
ans =
0
>> (5>=0)|(4>=-1)
ans =
1
>>
(5>=0)&(4
=-1)
ans =
0
>> xor((5>1),(4>0))
ans =
0
>> xor((5>1),(4б0))
xor((5>1),(4б0))
↑
Error: The input character is not valid in MATLAB statements or expressions.
>> xor((5>1),(4<0))
ans =
1
>> 4*i > 5*i
ans =
0
>> exp(pi) > pi^exp(1)
ans =
1
>> (2+10*i)>(3-2*i)
ans =
0
>>
>>
>>
>> % завдання: обчислення логічних виразів для матриць
>> M1=[2 0; -1 2];
>> M2=[-1 0; -2 2];
>> M1>M2
ans =
1 0
1 0
>>
((M1+M2)>=(M2-M1))
ans =
0 0
1 0
>> all(M1>M2)
ans =
1 0
>> any(M1>M2)
ans =
1 0
>>
((M1.*M2)>=(M2-M1))
ans =
0 0
0 0
>>
((M1.*M2)>=((M2-M1).*M2))
ans =
1 0
0 0
>> M1.^2>=M2.^2
ans =
1 1
0 1
>> M1.^2<=M2.^2
ans =
0 1
1 1
>> M1.\2<=M2.\2
ans =
0 1
1 1
>> M1./2<=M2./2
ans =
0 1
0 1
>> M1.\2==M2.\2
ans =
0 1
0 1
>> M1.\2==M2.\M2
ans =
1 0
0 1
>> M1./2<=M2./M2
ans =
1 0
1 1
>> M1./2<=M2./M1
ans =
0 0
1 1
>> M1.\M2==M2.\M1
ans =
0 0
0 1
>> M1.\M2<=M2.\M1
ans =
0 0
0 1
>> M1.\M2
=M2.\M1
>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
(5==10)&(7>1)
ans =
1
>> %%----------------------
>>
>> % Завдання: логічні оператори
>>
(5==10)&(7>1)
ans =
1
>> (4==5)|(1
=2)
ans =
1
>> (4>=5)|(2
=2)
ans =
0
>> (5>=0)|(4>=-1)
ans =
1
>>
(5>=0)&(4
=-1)
ans =
0
>> xor((5>1),(4>0))
ans =
0
>> xor((5>1),(4б0))
xor((5>1),(4б0))
↑
Error: The input character is not valid in MATLAB statements or expressions.
>> xor((5>1),(4<0))
ans =
1
>> 4*i > 5*i
ans =
0
>> exp(pi) > pi^exp(1)
ans =
1
>> (2+10*i)>(3-2*i)
ans =
0
>>
>>
>>
>> % завдання: обчислення логічних виразів для матриць
>> M1=[2 0; -1 2];
>> M2=[-1 0; -2 2];
>> M1>M2
ans =
1 0
1 0
>>
((M1+M2)>=(M2-M1))
ans =
0 0
1 0
>> all(M1>M2)
ans =
1 0
>> any(M1>M2)
ans =
1 0
>>
((M1.*M2)>=(M2-M1))
>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
(5==10)&(7>1)
ans =
1
>> %%----------------------
>>
>> % Завдання: логічні оператори
>>
(5==10)&(7>1)
ans =
1
>> (4==5)|(1
=2)
ans =
1
>> (4>=5)|(2
=2)
ans =
0
>> (5>=0)|(4>=-1)
ans =
1
>>
(5>=0)&(4
=-1)
>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
(5==10)&(7>1)
ans =
1
>> %%----------------------
>>
>> % Завдання: логічні оператори
>>
(5==10)&(7>1)
ans =
1
>> (4==5)|(1
=2)
ans =
1
>> (4>=5)|(2
=2)
>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
(5==10)&(7>1)
ans =
1
>> %%----------------------
>>
>> % Завдання: логічні оператори
>>
(5==10)&(7>1)>> % -- Гуменюк Богдан, ПМ-41 --
>> % -- Лабораторна робота №4 --
>> % завдання 4
>> A = [8, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 5, 6, -3, 4, 4];
>> B = [3, 10, 5,-6, 18, 14, 13, -4, 2, 3, 5, 6, -3, 4, 4, 6];
>> C = [9, 1, -5, 6, 8, 4, 3, -4, 2, 3, 5, -1, 8, 7, -3, 4, 4];
>> D = [5, 5, 3, 6, 8, -4, 7, 9, 4, -2, 13, 5, 1, 9, 5, 3, 8, 4];
>> E = [5, 3, 2, 9, 8, 4, 7, 3, 2, 9, 2, 4, 3, 7, 4, 6, 9, 7, 3];
>> F = [2, 6, 5, 6, 7, 7, 9, 4, 2, 3, 7, 1, 7, 2, 4, 8, 5];
>>
>> % розмірність векторів
>> length(A)
ans =
17
>> length(B)
ans =
16
>> length(C)
ans =
17
>> length(D)
ans =
18
>> length(E)
ans =
19
>> length(F)
ans =
17
>> % сума
>> sum(A)
ans =
46
>> sum(B)
ans =
80
>> sum(C)
ans =
51
>> sum(D)
ans =
89
>> sum(E)
ans =
97
>> sum(F)
ans =
85
>> % добуток
>> prod(A)
ans =
3.9813e+09
>> prod(B)
ans =
-6.1138e+11
>> sum(C)
ans =
51
>> prod(C)
ans =
8.3608e+09
>> prod(D)
ans =
2.0379e+12
>> prod(E)
ans =
2.4888e+12
>> prod(F)
ans =
5.9745e+10
>> % мінімальний елемент
>> min(A)
ans =
-5
>> min(B)
ans =
-6
>> min(C)
ans =
-5
>> min(D)
ans =
-4
>> min(E)
ans =
2
>> min(F)
ans =
1
>> % максимальний елемент
>> max(A)
ans =
8
>> min(B)
ans =
-6
>> % максимальний елемент
>> max(A)
ans =
8
>> max(B)
ans =
18
>> max(C)
ans =
9
>> max(D)
ans =
13
>> max(E)
ans =
9
>> max(F)
ans =
9
>> % середнє значення
>> mean(A)
ans =
2.7059
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % середньоквадратичне відхилення
>> std(A)
ans =
3.9333
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення медіани
>> median(A)
ans =
4
>> mean(B)
ans =
5
>> mean(C)
ans =
3
>> mean(D)
ans =
4.9444
>> mean(E)
ans =
5.1053
>> mean(F)
ans =
5
>> % обчислення комулятитивної суми
>> cumsum(A)
ans =
8 9 4 10 18 22 25 21 23 26 31 30 35 41 38 42 46
>> cumsum(B)
ans =
3 13 18 12 30 44 57 53 55 58 63 69 66 70 74 80
>> cumsum(C)
ans =
9 10 5 11 19 23 26 22 24 27 32 31 39 46 43 47 51
>> cumsum(D)
ans =
5 10 13 19 27 23 30 39 43 41 54 59 60 69 74 77 85 89
>> cumsum(E)
ans =
5 8 10 19 27 31 38 41 43 52 54 58 61 68 72 78 87 94 97
>> cumsum(F)
ans =
2 8 13 19 26 33 42 46 48 51 58 59 66 68 72 80 85
>> % різниця двох сусідніх елементів
>> diff(A)
ans =
-7 -6 11 2 -4 -1 -7 6 1 2 -6 6 1 -9 7 0
>> diff(B)
ans =
7 -5 -11 24 -4 -1 -17 6 1 2 1 -9 7 0 2
>> diff(C)
ans =
-8 -6 11 2 -4 -1 -7 6 1 2 -6 9 -1 -10 7 0
>> diff(D)
ans =
0 -2 3 2 -12 11 2 -5 -6 15 -8 -4 8 -4 -2 5 -4
>> diff(E)
ans =
-2 -1 7 -1 -4 3 -4 -1 7 -7 2 -1 4 -3 2 3 -2 -4
>> diff(F)
ans =
4 -1 1 1 0 2 -5 -2 1 4 -6 6 -5 2 4 -3
>> % сортування від меншого до більшого
>> sort(A)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 5 6 6 8 8
>> sort(B)
ans =
-6 -4 -3 2 3 3 4 4 5 5 6 6 10 13 14 18
>> sort(C)
ans =
-5 -4 -3 -1 1 2 3 3 4 4 4 5 6 7 8 8 9
>> sort(D)
ans =
-4 -2 1 3 3 4 4 5 5 5 5 6 7 8 8 9 9 13
>> sort(E)
ans =
2 2 2 3 3 3 3 4 4 4 5 6 7 7 7 8 9 9 9
>> sort(F)
ans =
1 2 2 2 3 4 4 5 5 6 6 7 7 7 7 8 9
>> % сортування від більшого до меншого
>> sort(A, 'descend')
ans =
8 8 6 6 5 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(B, 'descend')
ans =
18 14 13 10 6 6 5 5 4 4 3 3 2 -3 -4 -6
>> sort(C, 'descend')
ans =
9 8 8 7 6 5 4 4 4 3 3 2 1 -1 -3 -4 -5
>> sort(D, 'descend')
ans =
13 9 9 8 8 7 6 5 5 5 5 4 4 3 3 1 -2 -4
>> sort(E, 'descend')
ans =
9 9 9 8 7 7 7 6 5 4 4 4 3 3 3 3 2 2 2
>> sort(F, 'descend')
ans =
9 8 7 7 7 7 6 6 5 5 4 4 3 2 2 2 1
>>
>>
>>
>>
>>
>> % Завдання 2
>> A1 = [2 3 10; 4 6 5; 10 12 3];
>> B1 = [-5 6 1; 4 5 5; 12 1 -4];
>> C1 = [3 6 3; 4 0 -5; 20 13 8];
>> D1 = [-3 -6 3; 4 -5 5; 2 13 -8];
>> E1 = [-2 7 10; 4 4 -5; -10 12 -3];
>> F1 = [-5 -6 10; 4 -5 15; 1 1 6];
>> G1 = [2 2 3; 4 4 5; 2 3 8];
>> H1 = [3 4 3; 4 0 5; 0 3 4];
>> K1 = [2 7 0; 4 4 5; 1 2 3];
>> Q1 = [5 6 0; 4 5 5; 1 1 0];
>> X1 = [2 5 4; 4 0 5; 1 2 6];
>> V1 = [2 4 7; 0 3 8; 0 3 4];
>> M1 = [6 3 5; 1 2 6; 1 3 4];
>>
>> % визначник
>> det(A1)
ans =
-90.0000
>> det(B1)
ans =
525
>> det(C1)
ans =
-441.0000
>> det(D1)
ans =
9.0000
>> det(E1)
ans =
1218
>> det(F1)
ans =
369.0000
>> det(G1)
ans =
2
>> det(H1)
ans =
-73
>> det(K1)
ans =
-45
>> det(M1)
ans =
-49
>> det(Q1)
ans =
5.0000
>> det(V1)
ans =
-24
>> det(X1)
ans =
-83
>> % обернена матриця
>> inv(A1)
ans =
0.4667 -1.2333 0.5000
-0.4222 1.0444 -0.3333
0.1333 -0.0667 0
>> inv(B1)
ans =
-0.0476 0.0476 0.0476
0.1448 0.0152 0.0552
-0.1067 0.1467 -0.0933
>> inv(C1)
ans =
-0.1474 0.0204 0.0680
0.2993 0.0816 -0.0612
-0.1179 -0.1837 0.0544
>> inv(D1)
ans =
-2.7778 -1.0000 -1.6667
4.6667 2.0000 3.0000
6.8889 3.0000 4.3333
>> inv(E1)
ans =
0.0394 0.1158 -0.0616
0.0509 0.0870 0.0246
0.0722 -0.0378 -0.0296
>> inv(F1)
ans =
-0.1220 0.1247 -0.1084
-0.0244 -0.1084 0.3117
0.0244 -0.0027 0.1328
>> inv(G1)
ans =
8.5000 -3.5000 -1.0000
-11.0000 5.0000 1.0000
2.0000 -1.0000 0
>> inv(H1)
ans =
0.2055 0.0959 -0.2740
0.2192 -0.1644 0.0411
-0.1644 0.1233 0.2192
>> inv(K1)
ans =
-0.0444 0.4667 -0.7778
0.1556 -0.1333 0.2222
-0.0889 -0.0667 0.4444
>> inv(M1)
ans =
0.2041 -0.0612 -0.1633
-0.0408 -0.3878 0.6327
-0.0204 0.3061 -0.1837
>> inv(Q1)
ans =
-1.0000 0 6.0000
1.0000 0 -5.0000
-0.2000 0.2000 0.2000
>> inv(V1)
ans =
0.5000 -0.2083 -0.4583
0 -0.3333 0.6667
0 0.2500 -0.2500
>> inv(X1)
ans =
0.1205 0.2651 -0.3012
0.2289 -0.0964 -0.0723
-0.0964 -0.0120 0.2410
>> % норма матриці
>> norm(A1)
ans =
19.1968
>> norm(B1)
ans =
13.8696
>> norm(C1)
ans =
26.0290
>> norm(D1)
ans =
18.0802
>> norm(E1)
ans =
17.1020
>> norm(F1)
ans =
20.2312
>> norm(G1)
ans =
12.0176
>> norm(H1)
ans =
9.0356
>> norm(K1)
ans =
10.0895
>> norm(M1)
ans =
11.0637
>> norm(Q1)
ans =
10.7386
>> norm(V1)
ans =
12.7606
>> norm(X1)
ans =
10.3820
>> % власні значення
>> eig(A1)
ans =
18.2006
-7.8320
0.6314
>> eig(B1)
ans =
-6.6284 + 3.5749i
-6.6284 - 3.5749i
9.2568 + 0.0000i
>> eig(C1)
ans =
-5.0833 + 0.0000i
8.0416 + 4.6997i
8.0416 - 4.6997i
>> eig(D1)
ans =
0.2496
-2.6516
-13.5980
>> eig(E1)
ans =
-4.0000 +12.5698i
-4.0000 -12.5698i
7.0000 + 0.0000i
>> eig(F1)
ans =
7.4589 + 0.0000i
-5.7295 + 4.0797i
-5.7295 - 4.0797i
>> eig(G1)
ans =
11.7086
0.0771
2.2143
>> eig(H1)
ans =
-3.6564
2.4256
8.2308
>> eig(K1)
ans =
9.7572
-2.5593
1.8021
>> eig(M1)
ans =
9.5904
3.7662
-1.3566
>> eig(Q1)
ans =
10.4295 + 0.0000i
-0.2147 + 0.6583i
-0.2147 - 0.6583i
>> eig(V1)
ans =
2.0000
-1.4244
8.4244
>> eig(X1)
ans =
9.4010
2.3523
-3.7533
>> % lu розкладання матриць
>> lu(A1)
ans =
10.0000 12.0000 3.0000
0.4000 1.2000 3.8000
0.2000 0.5000 7.5000
>> lu(B1)
ans =
12.0000 1.0000 -4.0000
-0.4167 6.4167 -0.6667
0.3333 0.7273 6.8182
>> lu(C1)
ans =
20.0000 13.0000 8.0000
0.1500 4.0500 1.8000
0.2000 -0.6420 -5.4444
>> lu(D1)
ans =
4.0000 -5.0000 5.0000
0.5000 15.5000 -10.5000
-0.7500 -0.6290 0.1452
>> lu(E1)
ans =
-10.0000 12.0000 -3.0000
-0.4000 8.8000 -6.2000
0.2000 0.5227 13.8409
>> lu(F1)
ans =
-5.0000 -6.0000 10.0000
-0.8000 -9.8000 23.0000
-0.2000 0.0204 7.5306
>> lu(G1)
ans =
4.0000 4.0000 5.0000
0.5000 1.0000 5.5000
0.5000 0 0.5000
>> lu(H1)
ans =
4.0000 0 5.0000
0.7500 4.0000 -0.7500
0 0.7500 4.5625
>> lu(K1)
ans =
4.0000 4.0000 5.0000
0.5000 5.0000 -2.5000
0.2500 0.2000 2.2500
>> lu(M1)
ans =
6.0000 3.0000 5.0000
0.1667 2.5000 3.1667
0.1667 0.6000 3.2667
>> lu(Q1)
ans =
5.0000 6.0000 0
0.2000 -0.2000 0
0.8000 -1.0000 5.0000
>> lu(V1)
ans =
2 4 7
0 3 8
0 1 -4
>> lu(X1)
ans =
4.0000 0 5.0000
0.5000 5.0000 1.5000
0.2500 0.4000 4.1500
>> % QU розкладання матриць
>> qu(A1)
Undefined function or variable 'qu'.
>>
>>
>>
>>
>> % QR розкладання матриць
>> qr(A1)
ans =
-10.9545 -13.6931 -6.3901
0.3088 -1.2247 -6.9402
0.7719 -0.4279 -6.7082
>> qr(B1)
ans =
13.6015 0.1470 -2.4262
-0.2150 -7.8726 -3.4749
-0.6451 0.3380 -4.9029
>> qr(C1)
ans =
-20.6155 -13.4850 -7.2276
0.1694 4.8120 5.0990
0.8469 0.4317 4.4455
>> qr(D1)
ans =
5.3852 4.4567 -0.9285
-0.4770 14.4961 -9.8552
-0.2385 -0.4291 0.1153
>> qr(E1)
ans =
10.9545 -10.7719 -0.9129
-0.3088 -9.6419 -0.4321
0.7719 -0.0898 -11.5317
>> qr(F1)
ans =
6.4807 1.6973 2.4689
-0.3484 7.6889 -17.3225
-0.0871 -0.0214 7.4052
>> qr(G1)
ans =
-4.8990 -5.3072 -8.5732
0.5798 0.9129 4.9295
0.2899 -0.7669 -0.4472
>> qr(H1)
ans =
-5.0000 -2.4000 -5.8000
0.5000 4.3863 2.2980
0 -0.3954 3.3285
>> qr(K1)
ans =
-4.5826 -6.9830 -5.0190
0.6077 4.4987 -2.0112
0.1519 0.0138 2.1828
>> qr(M1)
ans =
-6.1644 -3.7311 -6.4889
0.0822 -2.8423 -5.2033
0.0822 0.5704 -2.7966
>> qr(Q1)
ans =
-6.4807 -7.8695 -3.0861
0.3484 -0.2673 -2.6726
0.0871 -0.4783 2.8868
>> qr(V1)
ans =
2.0000 4.0000 7.0000
0 -4.2426 -8.4853
0 0.4142 -2.8284
>> qr(X1)
ans =
-4.5826 -2.6186 -7.4194
0.6077 4.7056 2.6716
0.1519 -0.0903 3.8490
>>
>>
>>
>>
>>
>> % Завдання 6\
>> % Завдання 6
>> X = [5 3 -8 12; 2 -5 17 -6; -5 12 -4 13; 25 -3 -8 11];
>> Y = [25; 13; 11; 20];
>> Z = X\Y;
>> res = X*Z
res =
25
13
11
20
>> X = [8 1 -5 13; 12 -10 7 -6; 3 8 -7 13; 1 -7 1 1];
>> Y = [14; 10; 25; 50];
>> Z = X\Y;
>> res2 = X*Z
res2 =
14.0000
10.0000
25.0000
50.0000
>> X = [1 1 -7 13; 1 -5 7 -1; 4 13 -1 17; 5 3 -8 1];
>> Y = [5; 3; 1; 21];
>> Z = X\Y;
>> res3 = X*Z
res3 =
5.0000
3.0000
1.0000
21.0000
>> X = [1 2 -5 3; 2 -1 7 -6; 3 8 -7 3; 3 -1 1 1];
>> Y = [4; 1; 5; 7];
>> Z = X\Y;
>> res4 = X*Z
res4 =
4.0000
1.0000
5.0000
7.0000
>>
>>
>>
>>
>>
ans =
1
>> (4==5)|(1
ans =
0
>> (5>=0)|(4>=-1)
ans =
1
>>
ans =
0
>> xor((5>1),(4>0))
ans =
0
>> xor((5>1),(4б0))
xor((5>1),(4б0))
↑
Error: The input character is not valid in MATLAB statements or expressions.
>> xor((5>1),(4<0))
ans =
1
>> 4*i > 5*i
ans =
0
>> exp(pi) > pi^exp(1)
ans =
1
>> (2+10*i)>(3-2*i)
ans =
0
>>
>>
>>
>> % завдання: обчислення логічних виразів для матриць
>> M1=[2 0; -1 2];
>> M2=[-1 0; -2 2];
>> M1>M2
ans =
1 0
1 0
>>
ans =
0 0
0 0
>>
ans =
1 1
1 0
>>
>>
>>
>> % завдання: знайти значення функції
>> x=0:0.1:10;
>> f = (x.^2-sqrt(x))./(x.^3*1)
f =
Columns 1 through 13
NaN -306.2278 -50.9017 -16.9527 -7.3821 -3.6569 -1.9194 -1.0107 -0.4969 -0.1902 0 0.1211 0.1994
Columns 14 through 26
0.2503 0.2831 0.3038 0.3162 0.3228 0.3255 0.3254 0.3232 0.3197 0.3152 0.3101 0.3046 0.2988
Columns 27 through 39
0.2929 0.2869 0.2809 0.2750 0.2692 0.2635 0.2579 0.2525 0.2472 0.2421 0.2371 0.2323 0.2276
Columns 40 through 52
0.2231 0.2188 0.2145 0.2104 0.2065 0.2026 0.1989 0.1954 0.1919 0.1885 0.1853 0.1821 0.1791
Columns 53 through 65
0.1761 0.1732 0.1704 0.1677 0.1651 0.1625 0.1601 0.1577 0.1553 0.1531 0.1508 0.1487 0.1466
Columns 66 through 78
0.1446 0.1426 0.1406 0.1388 0.1369 0.1351 0.1334 0.1317 0.1300 0.1284 0.1268 0.1253 0.1238
Columns 79 through 91
0.1223 0.1209 0.1195 0.1181 0.1168 0.1154 0.1142 0.1129 0.1117 0.1105 0.1093 0.1081 0.1070
Columns 92 through 101
0.1059 0.1048 0.1037 0.1027 0.1017 0.1007 0.0997 0.0987 0.0978 0.0968
>>
>> x=-5:0.1:5;
>> f = (sqrt(x.^2-15))./(x.^3+1).^(1/3)
f =
Columns 1 through 7
0.3171 - 0.5492i 0.3072 - 0.5320i 0.2963 - 0.5131i 0.2842 - 0.4922i 0.2707 - 0.4689i 0.2555 - 0.4426i 0.2382 - 0.4126i
Columns 8 through 14
0.2181 - 0.3778i 0.1943 - 0.3366i 0.1649 - 0.2856i 0.1257 - 0.2176i 0.0591 - 0.1023i 0.1716 + 0.0991i 0.2697 + 0.1557i
Columns 15 through 21
0.3461 + 0.1998i 0.4136 + 0.2388i 0.4765 + 0.2751i 0.5371 + 0.3101i 0.5966 + 0.3444i 0.6560 + 0.3787i 0.7161 + 0.4134i
Columns 22 through 28
0.7774 + 0.4488i 0.8406 + 0.4853i 0.9062 + 0.5232i 0.9750 + 0.5629i 1.0475 + 0.6048i 1.1247 + 0.6493i 1.2073 + 0.6971i
Columns 29 through 35
1.2967 + 0.7486i 1.3941 + 0.8049i 1.5015 + 0.8669i 1.6213 + 0.9360i 1.7567 + 1.0142i 1.9125 + 1.1042i 2.0958 + 1.2100i
Columns 36 through 42
2.3177 + 1.3381i 2.5981 + 1.5000i 2.9757 + 1.7180i 3.5450 + 2.0467i 4.6491 + 2.6842i 0.0000 + Infi 0.0000 + 5.8211i
Columns 43 through 49
0.0000 + 4.8132i 0.0000 + 4.3817i 0.0000 + 4.1495i 0.0000 + 4.0154i 0.0000 + 3.9381i 0.0000 + 3.8967i 0.0000 + 3.8782i
Columns 50 through 56
0.0000 + 3.8730i 0.0000 + 3.8730i 0.0000 + 3.8704i 0.0000 + 3.8576i 0.0000 + 3.8272i 0.0000 + 3.7734i 0.0000 + 3.6927i
Columns 57 through 63
0.0000 + 3.5848i 0.0000 + 3.4526i 0.0000 + 3.3016i 0.0000 + 3.1385i 0.0000 + 2.9698i 0.0000 + 2.8007i 0.0000 + 2.6354i
Columns 64 through 70
0.0000 + 2.4765i 0.0000 + 2.3256i 0.0000 + 2.1832i 0.0000 + 2.0496i 0.0000 + 1.9244i 0.0000 + 1.8073i 0.0000 + 1.6975i
Columns 71 through 77
0.0000 + 1.5945i 0.0000 + 1.4976i 0.0000 + 1.4061i 0.0000 + 1.3196i 0.0000 + 1.2374i 0.0000 + 1.1590i 0.0000 + 1.0839i
Columns 78 through 84
0.0000 + 1.0116i 0.0000 + 0.9416i 0.0000 + 0.8734i 0.0000 + 0.8067i 0.0000 + 0.7407i 0.0000 + 0.6750i 0.0000 + 0.6087i
Columns 85 through 91
0.0000 + 0.5410i 0.0000 + 0.4702i 0.0000 + 0.3940i 0.0000 + 0.3073i 0.0000 + 0.1957i 0.1168 + 0.0000i 0.2487 + 0.0000i
Columns 92 through 98
0.3266 + 0.0000i 0.3851 + 0.0000i 0.4326 + 0.0000i 0.4727 + 0.0000i 0.5073 + 0.0000i 0.5377 + 0.0000i 0.5647 + 0.0000i
Columns 99 through 101
0.5890 + 0.0000i 0.6109 + 0.0000i 0.6308 + 0.0000i
>>
>> x=2:0.2:20;
>> f = (sqrt(x.^3.-20.*x.^2.+15.^x-5))./(sqrt(x.^3.+2.*x+1)+sqrt(x.^3-10))
f =
1.0e+09 *
Columns 1 through 7
0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 8 through 14
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 15 through 21
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 22 through 28
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 29 through 35
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 36 through 42
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Columns 43 through 49
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0001 + 0.0000i 0.0001 + 0.0000i 0.0001 + 0.0000i
Columns 50 through 56
0.0001 + 0.0000i 0.0001 + 0.0000i 0.0002 + 0.0000i 0.0002 + 0.0000i 0.0003 + 0.0000i 0.0004 + 0.0000i 0.0005 + 0.0000i
Columns 57 through 63
0.0006 + 0.0000i 0.0008 + 0.0000i 0.0010 + 0.0000i 0.0013 + 0.0000i 0.0016 + 0.0000i 0.0021 + 0.0000i 0.0027 + 0.0000i
Columns 64 through 70
0.0034 + 0.0000i 0.0044 + 0.0000i 0.0057 + 0.0000i 0.0073 + 0.0000i 0.0094 + 0.0000i 0.0121 + 0.0000i 0.0155 + 0.0000i
Columns 71 through 77
0.0200 + 0.0000i 0.0257 + 0.0000i 0.0331 + 0.0000i 0.0426 + 0.0000i 0.0549 + 0.0000i 0.0707 + 0.0000i 0.0911 + 0.0000i
Columns 78 through 84
0.1174 + 0.0000i 0.1513 + 0.0000i 0.1950 + 0.0000i 0.2514 + 0.0000i 0.3242 + 0.0000i 0.4181 + 0.0000i 0.5394 + 0.0000i
Columns 85 through 91
0.6959 + 0.0000i 0.8979 + 0.0000i 1.1589 + 0.0000i 1.4959 + 0.0000i 1.9313 + 0.0000i 2.4937 + 0.0000i 3.2205 + 0.0000i
>>
>> x = 1:0.5:15;
>> f = (sqrt(x.^3-5)+((x.^3+5).^(1/3)).^2)./(sqrt(x.^3+2.*x+1)+(sqrt(x.^3-10)).^3)
f =
Columns 1 through 7
-0.0647 + 0.1271i -0.0353 + 0.2475i 1.2466 + 0.9779i 0.5992 + 0.0000i 0.1945 + 0.0000i 0.0989 + 0.0000i 0.0604 + 0.0000i
Columns 8 through 14
0.0409 + 0.0000i 0.0294 + 0.0000i 0.0221 + 0.0000i 0.0172 + 0.0000i 0.0137 + 0.0000i 0.0111 + 0.0000i 0.0092 + 0.0000i
Columns 15 through 21
0.0077 + 0.0000i 0.0065 + 0.0000i 0.0056 + 0.0000i 0.0049 + 0.0000i 0.0042 + 0.0000i 0.0037 + 0.0000i 0.0033 + 0.0000i
Columns 22 through 28
0.0029 + 0.0000i 0.0026 + 0.0000i 0.0023 + 0.0000i 0.0021 + 0.0000i 0.0019 + 0.0000i 0.0017 + 0.0000i 0.0016 + 0.0000i
Column 29
0.0015 + 0.0000i
>>
>> x = -5:0.5:15;
>> f=(sqrt(x.^3-5+10)+((x.^3+2.*x-5).^(1/3)).^2)./(sqrt(x.^3+2)+(sqrt(x.^3-10)).^3)
f =
Columns 1 through 7
-0.0220 - 0.0087i -0.0284 - 0.0111i -0.0371 - 0.0144i -0.0494 - 0.0191i -0.0658 - 0.0257i -0.0856 - 0.0345i -0.1009 - 0.0447i
Columns 8 through 14
-0.0917 - 0.0263i -0.0949 + 0.0026i -0.0891 + 0.0204i -0.0788 + 0.0280i -0.0671 + 0.0364i -0.0468 + 0.0643i 0.0323 + 0.2378i
Columns 15 through 21
1.2763 + 1.1416i 0.6153 + 0.0000i 0.1971 + 0.0000i 0.1001 + 0.0000i 0.0613 + 0.0000i 0.0414 + 0.0000i 0.0298 + 0.0000i
Columns 22 through 28
0.0224 + 0.0000i 0.0174 + 0.0000i 0.0138 + 0.0000i 0.0112 + 0.0000i 0.0093 + 0.0000i 0.0078 + 0.0000i 0.0066 + 0.0000i
Columns 29 through 35
0.0056 + 0.0000i 0.0049 + 0.0000i 0.0043 + 0.0000i 0.0037 + 0.0000i 0.0033 + 0.0000i 0.0029 + 0.0000i 0.0026 + 0.0000i
Columns 36 through 41
0.0024 + 0.0000i 0.0021 + 0.0000i 0.0019 + 0.0000i 0.0017 + 0.0000i 0.0016 + 0.0000i 0.0015 + 0.0000i
>>
>> x = 2:0.2:20;
>> f = (sqrt((x.^3-20).*(x-5)).^2)./(sqrt(x.^3+2.*x+1).*(x.^3-10).^(1/3))
f =
Columns 1 through 7
3.9624 - 6.8631i 7.5537 + 0.0000i 2.3180 + 0.0000i 0.6075 + 0.0000i -0.3515 + 0.0000i -0.9338 + 0.0000i -1.2794 + 0.0000i
Columns 8 through 14
-1.4597 + 0.0000i -1.5168 + 0.0000i -1.4781 + 0.0000i -1.3625 + 0.0000i -1.1834 + 0.0000i -0.9508 + 0.0000i -0.6724 + 0.0000i
Columns 15 through 21
-0.3539 + 0.0000i 0.0000 + 0.0000i 0.3856 + 0.0000i 0.8000 + 0.0000i 1.2406 + 0.0000i 1.7055 + 0.0000i 2.1931 + 0.0000i
Columns 22 through 28
2.7017 + 0.0000i 3.2303 + 0.0000i 3.7778 + 0.0000i 4.3432 + 0.0000i 4.9258 + 0.0000i 5.5249 + 0.0000i 6.1398 + 0.0000i
Columns 29 through 35
6.7701 + 0.0000i 7.4152 + 0.0000i 8.0747 + 0.0000i 8.7481 + 0.0000i 9.4352 + 0.0000i 10.1355 + 0.0000i 10.8488 + 0.0000i
Columns 36 through 42
11.5748 + 0.0000i 12.3132 + 0.0000i 13.0638 + 0.0000i 13.8263 + 0.0000i 14.6006 + 0.0000i 15.3864 + 0.0000i 16.1836 + 0.0000i
Columns 43 through 49
16.9920 + 0.0000i 17.8113 + 0.0000i 18.6415 + 0.0000i 19.4825 + 0.0000i 20.3339 + 0.0000i 21.1958 + 0.0000i 22.0679 + 0.0000i
Columns 50 through 56
22.9503 + 0.0000i 23.8426 + 0.0000i 24.7449 + 0.0000i 25.6570 + 0.0000i 26.5788 + 0.0000i 27.5101 + 0.0000i 28.4510 + 0.0000i
Columns 57 through 63
29.4013 + 0.0000i 30.3609 + 0.0000i 31.3297 + 0.0000i 32.3077 + 0.0000i 33.2947 + 0.0000i 34.2907 + 0.0000i 35.2955 + 0.0000i
Columns 64 through 70
36.3092 + 0.0000i 37.3316 + 0.0000i 38.3626 + 0.0000i 39.4023 + 0.0000i 40.4504 + 0.0000i 41.5071 + 0.0000i 42.5721 + 0.0000i
Columns 71 through 77
43.6454 + 0.0000i 44.7270 + 0.0000i 45.8167 + 0.0000i 46.9146 + 0.0000i 48.0206 + 0.0000i 49.1346 + 0.0000i 50.2566 + 0.0000i
Columns 78 through 84
51.3865 + 0.0000i 52.5242 + 0.0000i 53.6697 + 0.0000i 54.8230 + 0.0000i 55.9840 + 0.0000i 57.1526 + 0.0000i 58.3288 + 0.0000i
Columns 85 through 91
59.5126 + 0.0000i 60.7039 + 0.0000i 61.9027 + 0.0000i 63.1088 + 0.0000i 64.3224 + 0.0000i 65.5432 + 0.0000i 66.7714 + 0.0000i
>>
>> x = -5:0.5:15;
>> f=(sqrt((x.^3-20).*(x-5)).^2)./(sqrt(x.^3+2.*x+1).*(x.^3-10).^(1/3))
f =
1.0e+02 *
Columns 1 through 7
-0.2115 - 0.1221i -0.1971 - 0.1138i -0.1851 - 0.1069i -0.1764 - 0.1018i -0.1727 - 0.0997i -0.1772 - 0.1023i -0.1953 - 0.1127i
Columns 8 through 14
-0.2391 - 0.1380i -0.3469 - 0.2003i -1.2533 - 0.7236i 0.2321 - 0.4020i 0.1430 - 0.2477i 0.0913 - 0.1582i 0.0570 - 0.0988i
Columns 15 through 21
0.0396 - 0.0686i 0.0132 + 0.0000i -0.0093 + 0.0000i -0.0150 + 0.0000i -0.0136 + 0.0000i -0.0082 + 0.0000i 0.0000 + 0.0000i
Columns 22 through 28
0.0102 + 0.0000i 0.0219 + 0.0000i 0.0350 + 0.0000i 0.0493 + 0.0000i 0.0645 + 0.0000i 0.0807 + 0.0000i 0.0978 + 0.0000i
Columns 29 through 35
0.1157 + 0.0000i 0.1344 + 0.0000i 0.1539 + 0.0000i 0.1740 + 0.0000i 0.1948 + 0.0000i 0.2163 + 0.0000i 0.2384 + 0.0000i
Columns 36 through 41
0.2612 + 0.0000i 0.2845 + 0.0000i 0.3084 + 0.0000i 0.3329 + 0.0000i 0.3580 + 0.0000i 0.3836 + 0.0000i
>>