Chiziqli algebraik tenglamalar sistemasi va ularni yechish usullari

_{Chiziqli algebraik tenglamalar sistemasi va ularni yechish usullari}

Annotatsiya: Mazkur maqolada chiziqli algebraik tenglamalar sistemasi va ularni yechish usullari to’g’risida batafsil ma’lumot keltirilgan.
Kalit so’zlar: chiziqli tenglamalar sistemasi (ChTS), tenglamalar sistemasi yechishning qo’shish usuli, o’rniga qo’yish usuli, grafik usuli, yagona yechim, birgalikda bo’lgan sistema, aniqmas sistema, ekvivalent sistema, birgalikda bo’lmagan sistema, tenglamalar sistemasining iqtisodiyotda qo’llanilishi.

System of linear algebraic equations and methods of their solution

Abstract: This article provides detailed information on the system of linear algebraic equations and methods for solving them.
Keywords: system of linear equations (CTS), system of equations, addition method of substitution, substitution method, graphical method, single solution, cohesive system, indefinite system, equivalent system, non-cohesive system, the application of the system of equations in the economy.

1. 
   Chiziqli algebraik tenglamalar sistemasi va uning yechimi.
   

Ma’lumki, bir necha tenglamalar birgalikda qaralsa, ularga tenglamalar sistemasi deyiladi.
Quyidagi
_ a₁₁x₁  a₁₂ x₂  ...  a_1nx_n  b₁,
^ a x  a x  ...  a x  b ,
^ 21 1 22 2 2n n 2


^ ... ... ... ... ... ...

^_a_m1x₁  a_m2 x₂  ...  a_mnx_n  b_m
(1)

sistemaga ⁿ noma’lumli ^m ta chiziqli algebraik tenglamalar sistemasi (yoki

soddalik uchun chiziqli tenglamalar sistemasi) deyiladi. Bu yerda
a₁₁,a₁₂ , ,a_mn

sonlar (1) sistemaning koeffitsiyentlari, sonlar esa ozod hadlar deyiladi.
x₁, x₂ ,_…, x_n
lar noma’lumlar,
b₁,b₂ ,...,b_m

Tenglamalar sistemasi koeffisiyentlaridan tuzilgan
_ a₁₁ a₁₂ ... a_{1n }
^ a a ... a ^

A  ^
21 22 2n _

^ ... ... ... ... ^
 a a ... a ^
 m1 m2 mn 
matritsa tenglamalar sistemasining asosiy matritsasi deyiladi. Noma’lumlar

vektorini
X  (x , x ,..., x )^T
ustun vektor, ozod hadlarni
B  (b ,b ,...,b )^T
ustun

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