Chiziqli algebraik tenglamalar

Mustaqil echish uchun misollar

1. 
   Berilgan
   

_10x₁  2x₂  x₃  24

^x  4x  3x  8
^ 1 2 3

^2x  x  8x
 9

 1 2 3
chiziqli algebraik tenglamalar sistemasini Kramer usuli bilan eching.

2. 
   Berilgan
   

_x₁  2x₂  3x₃  4x₄  5
^2x  x  2x  3x  1
^ 1 2 3 4


_3x₁  2x₂  x₃  2x₄
^_4x₁  3x₂  2x₃  x₄
 1
 5

chiziqli algebraik tenglamalar sistemasini Kramer usuli bilan eching.

3. 
   Berilgan
   

_8x₁  x₂  5x₃  11
^x  4x  2x  6
^ 1 2 3

^2x  x  5x
 4

 1 2 3
chiziqli algebraik tenglamalar sistemasini Gauss usuli bilan eching.

4. 
   Berilgan
   

_x₁  2x₂  3x₃  2x₄  6
^x  x  2x  3x  8
^ 1 2 3 4


_3x₁  2x₂  x₃  2x₄
^_2x₁  3x₂  2x₃  x₄
 4
 8

chiziqli algebraik tenglamalar sistemasini Gauss usuli bilan eching.

5. 
   Berilgan
   

2	-3	5
1	2	0
4	1	3

matritsaga teskari matritsani aniqlang.

6. 
   Ushbu
   

_4x₁  x₂  2x₃  7
^2x  5x  x  6
^ 1 2 3
^x  2x  7x  2
 1 2 3
sistemani teskari matritsa usuli yordamida eching.

7. 
   Ushbu
   

_5x₁  x₂  2x₃  8
^x  4x  x  4
^ 1 2 3
^x  x  4x  4
 ^{1 2 3}

chiziqli algebraik tenglamalar sistemasini iteratsiya usuli yordamida 10^-2 aniqlikda eching.

8. 
   Ushbu
   


_100x₁  30x₂  70x₃  1
_15x₁  50x₂  5x₃  1
^6x  2x  20x  1
 ^{1 2 3}
sistema uchun iteratsiya jarayoni yaqinlashuvchi ekanlgini ko’rsating va echimni 10^-2 aniqlikda topish uchun nechta iteratsiya jarayonini bajarish kerak?

9. 
   Berilgan
   

_3x₁  x₂  x₃  2
^x  5x  x  8
^ 1 2 3
^2x  3x  1
 ^{1 3}
chiziqli algebraik tenglamalar sistemasini Zeydel usuli bilan eching.

Tayanch so’z va iboralar

Matritsa, birlik matritsa, algebraik to’ldiruvchi, analitik usul, sonli-analitik usul, iteratsiya usuli, teskari matritsa usuli, Gauss usuli, Kramer usuli, Zeydel usuli, ketma-ket yaqinlashish usuli.

Savollar:

1. 
   Chiziqli algebraik tenglamalar sistemasining yagona echimga ega bo’lish sharti.
   

2. 
   Chiziqli algebraik tenglamalar sistemasini echishda Jordan usuli va uning algoritmi.
   
3. 
   Chiziqli algebraik tenglamalar sistemasini echishda iteratsiya usuli va uning algoritmi.
   
4. 
   Iteratsiya jarayonining yaqinlashish sharti.
   
5. 
   Chiziqli algebraik tenglamalar sistemasini echishda Zeydel usuli va uning algoritmi.
   
6. 
   Chiziqli algebraik tenglamalar sistemasini echishda ketma-ket yaqinlashish
   

usuli va uning algoritmi.