Задание 2!
>> A1=[2 3 -1;1 -1 3;3 5 1]
A1 =
2 3 -1
1 -1 3
3 5 1
>> b1=[2;-4;4]
b1 =
2
-4
4
>> disp(det(A1))
-16
>> x1=A1\b1
x1 =
-2
2
1/4503599627370495
>> disp(A1*x1)
2
-4
4
>> C1=inv(A1)
C1 =
1 1/2 -1/2
-1/2 -5/16 7/16
-1/2 1/16 5/16
>> C1*b1
ans =
-2
2
1/4503599627370496
**********************************************
>> A2=[4 3 -2;3 1 1;1 -2 -3]
A2 =
4 3 -2
3 1 1
1 -2 -3
>> b2=[-1;3;8]
b2 =
-1
3
8
>> disp(det(A2))
40
>> x2=A2\b2
x2 =
2
-3
-1/8188362958855448
>> disp(A2*x2)
-1
3
8
>> C2=inv(A2)
C2 =
-1/40 13/40 1/8
1/4 -1/4 -1/4
-7/40 11/40 -1/8
>> C2*b2
ans =
2
-3
0
**********************************************
A3 =
5 -2 1
2 1 2
1 -3 -1
>> b3=[-1;6;-5]
b3 =
-1
6
-5
>> disp(det(A3))
10
>> x3=A3\b3
x3 =
-1
0
4
>> disp(A3*x3)
-1
6
-5
>> C3=inv(A3)
C3 =
1/2 -1/2 -1/2
2/5 -3/5 -4/5
-7/10 13/10 9/10
>> C3*b3
ans =
-1
1/2251799813685248
4
**********************************************
>> A4=[3 3 2;2 +1 -1;1 -2 -3]
A4 =
3 3 2
2 1 -1
1 -2 -3
>> b4=[-1; 3; 4]
b4 =
-1
3
4
>> disp(det(A4))
-10
>> x4=A4\b4
x4 =
-1/3377699720527872
1
-2
>> disp(A4*x4)
-1
3
4
>> C4=inv(A4)
C4 =
1/2 -1/2 1/2
-1/2 11/10 -7/10
1/2 -9/10 3/10
>> C4*b4
ans =
0
1
-2
**********************************************
A5 =
2 -1 3
1 2 1
4 -3 -2
>> b5=[1;8;-1]
b5 =
1
8
-1
>> disp(det(A5))
-41
>> x5=A5\b5
x5 =
2
3
0
>> disp(A5*x5)
1
8
-1
>> C5=inv(A5)
C5 =
1/41 11/41 7/41
-6/41 16/41 -1/41
11/41 -2/41 -5/41
>> C5*b5
ans =
2
3
-1/72057594037927936
**********************************************
>> A6=[1 -2 1;2 1 3;3 4 1]
A6 =
1 -2 1
2 1 3
3 4 1
>> b6=[4;5;2]
b6 =
4
5
2
>> disp(det(A6))
-20
>> x6=A6\b6
x6 =
7/5
-4/5
1
>> disp(A6*x6)
4
5
2
>> C6=inv(A6)
C6 =
11/20 -3/10 7/20
-7/20 1/10 1/20
-1/4 1/2 -1/4
>> C6*b6
ans =
7/5
-4/5
1
**********************************************
>> A7=[2 -1 3;1 2 1;1 -3 4]
A7 =
2 -1 3
1 2 1
1 -3 4
>> b7=[3;2;-1]
b7 =
3
2
-1
>> disp(det(A7))
10
>> x7=A7\b7
x7 =
3
0
-1
>> disp(A7*x7)
3
2
-1
>> C7=inv(A7)
C7 =
11/10 -1/2 -7/10
-3/10 1/2 1/10
-1/2 1/2 1/2
>> C7*b7
ans =
3
1/12009599006321322
-1
**********************************************
>> A8=[3 1 -2;1 -2 3;2 3 -1]
A8 =
3 1 -2
1 -2 3
2 3 -1
>> b8=[1;5;-4]
b8 =
1
5
-4
>> disp(det(A8))
-28
>> x8=A8\b8
x8 =
1
-2
0
>> disp(A8*x8)
1
5
-4
>> C8=inv(A8)
C8 =
1/4 5/28 1/28
-1/4 -1/28 11/28
-1/4 1/4 1/4
>> C8*b8
ans =
1
-2
0
**********************************************
>> A9=[1 -3 -1;2 1 1;2 -1 -3]
A9 =
1 -3 -1
2 1 1
2 -1 -3
>> b9=[1;-7;5]
b9 =
1
-7
5
>> disp(det(A9))
-22
>> x9=A9\b9
x9 =
-2
0
-3
>> disp(A9*x9)
1
-7
5
>> C9=inv(A9)
C9 =
1/11 4/11 1/11
-4/11 1/22 3/22
2/11 5/22 -7/22
>> C9*b9
ans =
-2
1/9007199254740992
-3
**********************************************
>> A10=[3 1 2;1 -2 -1;2 3 2]
A10 =
3 1 2
1 -2 -1
2 3 2
>> b10=[-4;-1;0]
b10 =
-4
-1
0
>> disp(det(A10))
7
>> x10=A10\b10
x10 =
1/2251799813685248
2
-3
>> disp(A10*x10)
-4
-1
1/1125899906842624
>> C10=(A10)
C10 =
3 1 2
1 -2 -1
2 3 2
>> C10*b10
ans =
-13
-2
-11
**********************************************
>> A11=[1.2 1.06 0;4.2 -6.3 -0.9;0.6 6.8 -0.82]
A11 =
6/5 53/50 0
21/5 -63/10 -9/10
3/5 34/5 -41/50
>> b11=[2.12;-1.1;0.89]
b11 =
53/25
-11/10
89/100
>> disp(det(A11))
2327/140
>> x11=A11\b11
x11 =
3978/2989
630/1277
195/49
>> disp(A11*x11)
53/25
-11/10
89/100
>> C11=inv(A11)
C11 =
844/1243 163/3117 -201/3502
275/1574 -157/2652 1125/17314
788/405 -1425/3148 -787/1089
>> C11*b11
ans =
3978/2989
630/1277
195/49
**********************************************
>> A12=[6.5 2.34 1.4;0.5 7.3 -2.4;8.6 0.34 -6.4]
A12 =
13/2 117/50 7/5
1/2 73/10 -12/5
43/5 17/50 -32/5
>> b12=[2.8;-3.8;0.64]
b12 =
14/5
-19/5
16/25
>> disp(det(A12))
-10671/25
>> x12=A12\b12
x12 =
837/1810
-131/338
937/1871
>> disp(A12*x12)
14/5
-19/5
16/25
>> C12=inv(A12)
C12 =
747/6946 -263/7265 173/4663
99/2423 541/4305 -429/11234
367/2502 -81/1930 -148/1365
>> C12*b12
ans =
837/1810
-131/338
937/1871
**********************************************
>> A13=[6 0.13 -0.67; 3.8 1.25 -4.3; 0.38 -0.64 -3.2]
A13 =
6 13/100 -67/100
19/5 5/4 -43/10
19/50 -16/25 -16/5
>> b13=[1.9;6.4;5.4]
b13 =
19/10
32/5
27/5
>> disp(det(A13))
-5505/148
>> x13=A13\b13
x13 =
207/1301
-17/26
-569/370
>> disp(A13*x13)
19/10
32/5
27/5
>> C13=inv(A13)
C13 =
169/931 -205/9026 -43/5743
-519/1834 927/1820 -889/1422
298/3813 -481/4600 -579/3074
>> C13*b13
ans =
207/1301
-17/26
-569/370
**********************************************
>> A14=[0.63 -0.54 1.7; 0.65 4.4 0.15; 1.5 0.2 4.1]
A14 =
63/100 -27/50 17/10
13/20 22/5 3/20
3/2 1/5 41/10
>> b14=[3.6;2.3;2.8]
b14 =
18/5
23/10
14/5
>> disp(det(A14))
1257/755
>> x14=A14\b14
x14 =
7171/241
-3079/872
-1625/162
>> disp(A14*x14)
18/5
23/10
14/5
>> C14=inv(A14)
C14 =
1363/126 1623/1058 -2248/495
-702/479 330/16649 542/893
-1092/281 -809/1439 891/475
>> C14*b14
ans =
7171/241
-3079/872
-1625/162
**********************************************
>> A15=[12 4.2 -0.8;-4.1 2.2 -0.16;1.6 -4.3 8.4]
A15 =
12 21/5 -4/5
-41/10 11/5 -4/25
8/5 -43/10 42/5
>> b15=[-5.4; 1.6; 12.2]
b15 =
-27/5
8/5
61/5
>> disp(det(A15))
24551/71
>> x15=A15\b15
x15 =
-972/2513
206/1689
1104/695
>> disp(A15*x15)
-27/5
8/5
61/5
>> C15=inv(A15)
C15 =
154/2993 -794/8623 39/12395
303/3065 1066/3611 233/15494
75/1838 240/1423 674/5343
>> C15*b15
ans =
-972/2513
206/1689
1104/695