Yechishning matritsa, Gauss va Gauss-Jordan usullari

"Science and Education" Scientific Journal

August 2021 / Volume 2 Issue 8

Chiziqli algebraik tenglamalar sistemasini yechishning matritsa, Gauss va Gauss-Jordan usullari

Maxsud Tulqin o’g’li Usmonov [e-mail]

Toshkent axborot texnologiyalari universiteti Qarshi filiali


Annotatsiya: Chiziqli algebraaik tenglamalar tizimlarini echish usullarini ko’rib chiqiladi, unda tenglamalar soni noma’lum o’zgaruvchilar soniga teng va bitta echim mavjud. Birinchidan, biz ikkinchisiga e’tibor qaratamiz, ikkinchidan, biz tenglamalar tizimini echish usulini ko’rsatamiz, uchinchidan, Gauss usulini (noma’lum o’zgaruvchilarni izchil chiqarib tashlash usuli) tahlil qilamiz.
Kalit so’zlar: Chiziqli tenglamalar sistemasini yechishning Gauss usuli, chiziqli tenglamalar sistemasini yechishning Gauss - Jordan modifikatsiyasi, chiziqli tenglamalar sistemasining bazis yechimlari.

Matrix, Gauss and Gauss-Jordan methods for solving systems of linear algebraic equations

Mahsud Tulkin oglu Usmanov [e-mail]

Karshi branch of Tashkent University of Information Technologies


Abstract: A method of solving systems of linear algebraic equations is considered, in which the number of equations is equal to the number of unknown variables and there is only one solution. First, we focus on the second, second, we show a way to solve a system of equations, and third, we analyze the Gaussian method (a method of sequential subtraction of unknown variables).
Keywords: Gaussian method of solving systems of linear equations, Gaussian- Jordan modification of systems of linear equations, basic solutions of systems of linear equations.


1. Chiziqli algebraik tenglamalar sistemasini yechishning matritsa usuli.
Ushbu ⁿ noma’lumli ⁿ ta chiziqli algebraik tenglamalar sistemasi berilgan boʻlsin:

_ a₁₁x₁  a₁₂ x₂  ....  a_1nx_n  b₁,
^a x  a x  ....  a x  b ,
^ 21 1 22 2 2n n 2


^ ... ... ... ... ... ...

^_ a_n1x₁  a_n2 x₂  ....  a_nnx_n  b_n .
(1)

tenglamalar sistemada quyidagi belgilashlarni kiritamiz:

^{ a}11 ^a12
^ a a
...
...
^a_1n   ^x₁   ^b₁ 
_a   _x   _b 