2- laboratoriya mashg’uloti Matrisalarning asosiy xarakteristikalarini xisoblash

2 -1 0

3 0 1
>> A*B ans =

2 -1 1

-2 1 0
2 2 1
Endi shu amalni algoritmi haqida ya’ni o’z qo’limiz yordamida bajaramiz:
>> for i=1:3; for j=1:3; C(i,j)=0; for k=1:3; C(i,j)=C(i,j)+A(i,k)*B(k,j); end; end; end; C C =
2 -1 1
-2 1 0
2 2 1
2-Misol: A va B matritsalarni bir-biriga qo’shish
>> A=[-1 0 1; 0 -1 0; 1 -1 1];
>> B=[1 1 0; 2 -1 0; 3 0 1];
>> A+B ans =
0 1 1
2 -2 0
4 -1 2
Endi shu matritsalarni qo’shish amalini algoritmini o’zimiz bajarib ko’ramiz:
>> for i=1:3; for j=1:3; C(i,j)=A(i,j)+B(i,j);end; end; C
C =
0 1 1
2 -2 0
4 -1 2
3 – misol: Matlabda matritsalarni chapdan o’ngga burishda fliplr komandasidan foydalanish:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1

0. 
   -1 0
   
1. 
   1 -1 1 >> fliplr(A) ans =
   
2. 
   0 -1
   

0 -1 0

1 -1 1

Endi shu komandani qo’lda bajarib chiqamiz:
>> for i=1:3; for j=1:3; C(i,j)=A(3-i+1,j);end; end; C
C =
1 -1 1

0. 
   -1 0
   
1. 
   0 1
   

4 - misol: Matlabda matritsalarni yuqoridan pastga burishda flipud komandasidan foydalanish:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1

0. 
   -1 0
   
1. 
   -1 1
   

>> flipud(A) ans =

1 -1 1
0 -1 0 -
1 0 1
Endi shu amalni algoritmi bilan tanishib chiqamiz:
>> for i=1:3; for j=1:3; C(j,i)=A(j,3-i+1); end; end; C
C =
1 0 -1

0. 
   -1 0
   
1. 
   -1 1
   

5 – misol: Berilgan matritsani soat strelkasiga qarshi 90⁰ ga burish uchun ishlatiladigan rot90(A) komandasi:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1

0. 
   -1 0
   
1. 
   -1 1
   

>> rot90(A) ans =
1 0 1
0 -1 -1 -
1 0 1
Endi shu amalning bajarilish tartibi ya’ni algoritmi haqida:
>> for i=1:3; for j=1:3; C(i,j)=A(j,3-i+1); end; end; C
C =
1 0 1

0. 
   -1 -1
   
1. 
   0 1
   

Undan tashqari matlabda maxsus ko’rinishdagi matritsalarni hosil qilish imkoniyati bor. Ana shunday matritsalarni hosil qiluvchi komandalarni kyeltirib o’tamiz:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1

0. 
   -1 0
   
1. 
   -1 1
   

>> size(A) ans =
3 3
>> length(A)
ans = 3
>> ndims(A)
ans =
2
>> isempty(A) ans =
0
6 - misol: diag(A) komandasi berilgan matritsaning diagonalida tugan elementlarni ekranga chiqaradi:
>> A=[-1 0 1; 0 -1 0; 1 -1 1]
A =
-1 0 1

0. 
   -1 0
   
1. 
   -1 1
   

>> diag(A) ans =
-1 -1 1
Shu amalni o’zimiz bajarib chqamiz:
>> for i=1:3; D(i)=A(i,i);end; D
D =
-1 -1 1
7 – misol: eye(n) komandasi birlik matritsa hosil qilish:
>> eye(5) ans =
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0

0. 
   0 0 0 1
   

Endi shu matritsani m-faylga funksiyasini yaratamiz:

Ushbu m-faylga birlik matritsa hosil qiladigan protsedura yasadik va uning nomini diagonal.m deb nomladik. Endi bu m-fayl yordamida diagonal(n) komandasi hosil bo’ldi. Endi ushbu komanda yordamida ham eye(n) komandasining bajargan ishini bajarsa bo’ladi: >> diagonal(5) ans =

0. 
   0 0 0 0
   

0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
8-misol: Berilgan matritsaning diagonaildan yuqori qismini elementlarini 0 bilan almashtirish:
>> A=[-1 2 4 0 3; -2 1 0 3 4; -2 -1 0 -2 1; -2 3 -1 -1 1; 1 1 1 -1 -1]
A =