Science and Education

"Science and Education" Scientific Journal

August 2021 / Volume 2 Issue 8

Matritsa rangi. Matritsa rangini hisoblash usullari

Maxsud Tulqin o‘g’li Usmonov [e-mail]

Toshkent axborot texnologiyalari universiteti Qarshi filiali


Annotatsiya: Ixtiyoriy o’lchamli matritsaning bir necha satr yoki ustunlarini o chirishdanʻʻhosil bo‘lgan kvadrat matritsa determinantiga matritsa osti minori deyiladi. Bukvadrat matritsa tartibi matritsa osti minorning tartibi deyiladi. Agar berilganmatritsa kvadrat shaklda bo lsa, uningʻeng katta tartibli minori o zigaʻteng. Ixtiyoriy oʻlchamli matritsaning k ta satr va k ta ustunlarini ajratilgan boʻlib, bu satr va ustunlar kesishmalarida yotgan elementlaridan hosil bo‘lgan kvadrat matritsa determinantiga matritsaning k chi tartibli minori deyiladi.
Kalit so’zlar: Matritsa, k-chi tartibli minor, matritsa rangi, minorlar usuli, ekvivalent almashtirishlar.


Color matrix. Methods for calculating the color of the matrix

Mahsud Tulkin oglu Usmanov [e-mail]

Karshi branch of Tashkent University of Information Technologies


Abstract: The determinant of a square matrix formed by deleting several rows or columns of an arbitrary-sized matrix is called a sub-matrix. The order of the square matrix is called the order of the sub-matrix minor. If the given matrix is square, then its largest order of magnitude is zigzag. The determinant of a square matrix formed by the elements lying at the intersection of rows and columns, separated by k rows and k columns of an arbitrary dimensional matrix, is called the minor order minor of the matrix.
Keywords: Matrix, k-th minor, matrix color, minor method, equivalent substitutions.

Agar berilgan matritsa kvadrat shaklda boʻlsa, uning eng katta tartibli minori

oʻziga teng. Agar berilgan matritsa ^{n  m} chi tartibli boʻlsa, u holda uning eng katta

tartibli minorining tartibi
k  min(n, m)
boʻladi.

n m
Agar berilgan matritsa ^{n  m}
chi tartibli boʻlsa, u holda bu matritsadan ajratish

mumkin bolgan ^k tartibli minorlar sonini
C^k  C^k
formula bilan topiladi, bu erda



C
_k n!




va
ⁿ k! (n  k)!
_k m!






C
^m k! (m k)!
, n yoki m ta elementdan k tadan

gruppalashlar soni.

1. 
   Matritsa rangi ta’rifi va uning xossalari.
   

_ 4 5 7 7 _

 
A  ^ 2 1 4 3 ^
 3 7 0 8 ^
1-misol. ^{ } matritsaning minorlarini aniqlang.
Yechish.

1. 
   tartibli minorlar. Bu matritsaning ixtiyoriy elementi 1- tartibli minor tashkil qiladi. Demak bu matritsada 12 ta 1-tartibli minor bor.
   
2. 
   tartibli minorlar.
   

4 5
M ₂  _{2 1}
4 7
M ₂  _{2 4}
4 5
M ₂  _{3 7}
1 va 2-satrni, hamda 1 va 2-ustunlarni ajratishdan hosil qilingan. 1 va 2-satrni, hamda 1 va 3-ustunlarni ajratishdan hosil qilingan.
1 va 3-satrni, hamda 1 va 2-ustunlarni ajratishdan hosil qilingan.

Va hokazo shu tartibda davom qilib

C²  C² 