Mathcad muhitida chiziqli algebraik tenglamalar sistemalarini tadqiq etish va yechish

A ^1 4

2 ^

b ^3^
 
x A^{ 1}b

_3 1
1 _

¹

⁴ 
¹ 

_{ } x ^2^
lsolve (Ab) _2_{ }3_

x₁ 1;
_3  
x₂ 2; x₃ 3.

A ^1 4

2 ^

b ^3^
 

_3 1 1 _
⁴ 

 0.0005

Zeydel^Ab^
n cols(A) F A^TA H A^Tb

for
i  0 n  1

for
j  0 n  1

A_{i j}  0
if i j

^Ai j ^

i
H
F



F
i j



ii

otherwise

b_i _F
i i
k  0 x1 b
while 1
x  x1

for
i  0 n  1 s  0

for
j  0 n  1

s  s  A_ix
j j
x  s  b
i i
y  x  x1
x1  x
m  max(y) k  k  1

x A^{ 1}b
¹
x ^2 ^
break x k m
if ^m ^ (k  200)


³

^2,1x 1, 5x 19,8x 1, 3x
 28, 76

_ 1 2 3 4

^0, 9x  2, 5x 1, 3x  32,1x
 49, 72

 1 2 3 4

Echimi:


_20.9
_{A }1.2
^2.1
_^0.9

1.2
21.2

1.5
2.5


2.1
1.5
19.8
1.3


0.9 _
2.5_
1.3^
32.1^<sub>


</sub>21.7 _{b }27.46_
^28.76^
_49.72^_
x A^{ 1}b


_0.8 _{x }¹ 
^1.2^
_1.4^_

_0.8_
lsolve (Ab) ^1

x₁ 0.8;
^1.2^
_1.4^_
x₂ 1; x₃ 1.2;
x₄  1.4

Misol 5: Quydagi tizimni eching


_13,47x₁2,29x₂3,29x₃4,75x₄

2,32

^2, 75x 11,11x2, 28x 0, 75x
4,75

^ 1 2 3 4

^0,28x6,25x9,21x0,79x
2, 25

_ 1 2 3 4

^3, 21x 2, 21x0, 49x 7,87x
3, 41

 1 2 3 4


Echimi:

_13.47
2.29
3.29
4.75 _{
}2.32 _

A ^
2.75
11.11
2.28
0.75 _
b ^
4.75 _

^0.28
_^3.21
6.25
2.21
9.25 0.49


_
0.79^
7.87^_


0.493_
^2.25^
_3.41^_

lsolve (A b) ^
0.278 _

x₁ 0.493;
^0.101^
_0.706^_
x₂ 0.278; x₃ 0.101;
x₄ 0.706

Misol 6: Quydagi tizimni eching


_9,66x₁2,01x₂ 3,03x₃1,61x₄ 2,29
^3, 22x 12, 41x 1, 65x0, 93x2, 64
^ 1 2 3 4

_1, 69x₁  2,17x₂ 13, 65x₃  3, 73x₄ 6, 48
^0, 46x1, 75x 3, 75x9, 65x 2, 77
 1 2 3 4

Echimi:


_9.66
2.01
3.03


1.61 <sub>


</sub>2.29 <sub>


</sub>0.14 _

_{A }3.22
12.41
1.65
0.93 _
b ^
2.64 _
lsolve (A b) ^
0.32_

^1.69
2.17
13.65
3.73 ^
6.483 ^
0.284 ^

^_0.46
1.75
3.75
9.65 ^_
^2.77 ^_
^_0.449 ^_

_0.14 _

x A^{ 1}b
x ^
0.32 _

^0.284^
_0.449^_

x₁ 0.14;
x₂ 0.32; x₃ 0.284;
x₄ 0.449

Misol 7: Quydagi tizimni eching

^2, 28x  3, 48x 15, 78x  2, 64x
 2, 71

_ 1 2 3 4
^3, 41x  0, 51x 1, 07x  6, 07x  2, 33
 1 2 3 4

Echimi:


_15.75
2.91
3.60

2.09 _

_2.84 <sub>


</sub>0.418 _

A ^
3.63
12.02
6.71
0.09 _
b ^
9.81 _
lsolve (A b) ^
0.99 _

^2.28
_^3.41
3.48
0.51
15.78
1.07
2.64^
6.07^_
^2.71^
_^2.33^_
^0.078^
_^0.549^_

_0.418 _

x A^{ 1}b
x ^
0.99 _

^0.078^
_^0.549^_

x₁ 0.418;
x₂ 0.99; x₃ 0.078;
x₄  0.549

Misol 8: Quydagi tizimni eching


_0, 01x₁  2, 01x₂  4, 76x₃ 1, 01x₄  2, 23
^7, 27x 0, 09x1, 04x9, 27x 0, 91
^ 1 2 3 4

_10, 35x₁  2, 35x₂ 1, 28x₃  4, 01x₄  2, 08
^0, 49x 0, 28x 4, 35x1, 97 x 2, 61
 1 2 3 4


Echimi:

_0.01
2.01
4.76
1.01_{
}2.23 _{
}1.214 _

A ^
7.27
0.09
1.04
9.27_
b ^
0.91 _
lsolve (Ab) ^{2.848 }

^10.35
_^0.49
2.35
0.28
1.28
4.35
4.01^
1.97^_
^2.08^
_2.61^_
^0.575^
_0.762^_

_1.214 _

xA^1b
_x2.848_
^0.575^
_0.762^_

x₁ 1.214;
x₂ 2.848; x₃ 0.575;
x₄ 0.762.

Misol 9: Quydagi tizimni eching


_7, 71x₁  2,83x₂ 1, 08x₃  0, 75x₄  2, 23x₅  2, 39
^2, 93x3, 96x 14, 75x2, 75x 0, 91x 0.78
_ 1 2 3 4 5
_6, 36x₁  0, 78x₂  3, 75x₃ 14, 7x₄  2, 08x₅  2.83
^0, 48x3, 73x 0, 75x1, 09x 2, 61x 7, 38
_ 1 2 3 4 5
_0,93x₁1,23x₂11,21x₃7,69x₄3,75x₅0,34
Echimi:

_7.71
^2.93
2.83
3.96
1.08
14.75
0.75
2.75
2.23_
0.91^
_2.39_
^0.78^
_0.566_
^1.454^


A _6.36

0.78

3.75

14.7


2.08_

b _

2.83_

lsolve(Ab)_

0.312_

^0.48

_0.93
3.73
1.23
0.75
11.21
1.09
7.69
2.61^


3.75^
7.38^
 
_0.34_
^0.178^
 
_0.869_

_0.566_
^1.454^

x A
 1_b


x _

0.312_

^0.178^
 
_0.869_

x₁ 0.566;
x₂ 1.454; x₃ 0.312;
x₄ 0.178;
x₅  0.869.

Misol 10: Quydagi tizimni eching


_7, 71x₁  2,83x₂ 1, 08x₃  0, 75x₄  2, 23x₅  2, 39
^2, 93x 3, 96x14, 75x2, 75x0, 91x 0.78
_ 1 2 3 4 5
_6, 36x₁  0, 78x₂  3, 75x₃ 14, 7x₄  2, 08x₅  2.83
^0, 48x 3, 73x 0, 75x1, 09x2, 61x 7, 38
_ 1 2 3 4 5
_0,93x₁1,23x₂11,21x₃7,69x₄3,75x₅0,34
Echimi:

_4.75
^14.35
0.85 0.79
1.28
1.94
9.74
3.79
0.78_
2.85^
_1.29_
^3.29^
_1.062_
^2.735^


A_
9.66
2.01
3.03
1.61

2.29_

b_

0.71_

lsolve (Ab)_

1.546_

^3.63

_2.83
12.02
3.02
6.71
11.79
0.09 1.75
9.81^


2.71^
11.49^
 
_2.80_
^1.073^
 
_3.062_

_1.062_
^2.735^

x A
1_b


x_

1.546_

^1.073^
 
_3.062_

x₁ 1.062;
x₂ 2.735; x₃ 1.546;
x₄ 1.073;
x₅ 3.062.

Misol 11: Quydagi tizimni eching


_3, 75x₁  0, 28x₂ 1, 05x₃  0, 48x₄ 1, 28x₅  0.28x₆  4, 23
^0, 3x 3, 95x 3, 07x0, 57x3, 75x1, 31x  0.68
_ 1 2 3 4 5 6


_4,88x₁  0,88x₂  4, 75x₃  0, 07x₄  2, 08x₅  2.83x₆  2, 33
_3, 44x₁  2,88x₂  0, 75x₃  9, 79x₄  0, 28x₅  7, 38x₆ 9, 77


^18,88x₁  0, 29x₂ 1, 75x₃  3, 28x₄  4, 35x₅  0, 34x₆  2, 35
_4,75x₁19,29x₂10,37x₃0,73x₄0,47x₅8,78x₆0,47

Echimi:


x₁ 1.062;


x₂ 2.735; x₃ 1.546;


x₄ 1.073;


x₅ 3.062.





3.75	0.28	1.05	0.48	1.28	0.28 
0.3	3.95	3.07	0.57	3.75	1.31  
4.88	0.88	4.75	0.07	2.08	2.83 

A ^



b ^
4.23_
0.68^

2.33_

^3.44


^18.88
_4.75
2.88
0.29
19.29
0.75
1.75
10.37
9.79
3.28 0.73
0.28
4.35
0.47
7.38^


0.34^
8.78_
^9.77^




^2.35^
_0.47_

_1.868_{ }1.868_

^12.14 ^
 
^12.14 ^
 

x A^{ 1}b
x ^
5.854 _
lsolve (Ab) ^
5.854 _

^16.538^{ }16.538^








^ 0.92 ^{ } 0.92 ^
_17.377_{ }17.377_

x₁ 1.868;
x₂ 12.14; x₃ 5.854;
x₄ 16.538;
x₅  0.92; x₆ 17.377.

Misol 12: Quydagi tizimni eching [6]


_9, 77x₁  0, 37x₂ 1, 43x₃ 1, 34x₄  2, 33x₅  2.84x₆  2, 39
^3, 23x18, 91x 8, 71x 3, 73x 0, 78x 4, 48x 0, 33
_ 1 2 3 4 5 6
_4,88x₁  9, 77x₂ 12, 75x₃ 1, 72x₄  3, 78x₅  2.39x₆  6, 61
^0, 07x0, 75x  7, 23x  7, 96x 2,88x 12, 33x 4, 78
_ 1 2 3 4 5 6


^7, 71x₁  2,83x₂ 1, 08x₃  0, 75x₄  2, 39x₅  4, 54x₆ 6, 35
_0,77x₁16,61x₂8,91x₃2,61x₄6,62x₅3,32x₆4,5


Echimi:

_9.77
^3.23
0.37
18.91
1.43
8.71
1.34
3.73
2.33
0.78
2.84_
4.48^
_2.39_
^0.33^


_{A }4.88
^0.07


9.77
0.75

12.75
7.23

1.72
7.96


3.78
2.88

2.39_
12.33^

b ^


6.61_
4.78^


^7.71
_0.77
2.83
16.61
1.08
8.91
0.75
2.61
2.39
6.62
4.54^


3.32_
^6.35^

 
_4.5 _

_0.155_{ }0.155 _

x A^{ 1}b



x ^

0.541 ^

0.778 _
2.573 ^


lsolve (A b) ^

0.541 ^

0.778 _
2.573 ^

^1.323^{ }1.323^
   
_1.386_{ }1.386_

x₁ 0.155;
x₂ 0.541;
x₃ 0.778;
x₄ 2.573;
x₅ 1.323; x₆ 1.386.