1-amaliy mashg`ulot
Matritsalar. Asosiy tushuncha va ta’riflar. Matritsalar ustida amallar. Texnologik matritsa. Ishlab
chiqarishni optimal rejalashtirish masalasi va boshqa iqtisodiy masalalarni modellashtirishda
matritsalarning o‘rni.
Auditoriyada yechiladigan misollar.
 1 2
 2 5




1. A va B matrisalarning yig`indisini hisoblang. A   3 5  B   3 4 
 4 1
1 6




 1 2   2 5  1  2 2  5   3 7 

 
 
 

Yechish. A  B   3 5    3 4    3  3 5  4    6 9 
 4 1 1 6  4 1 1 6  5 7

 
 
 

 1 1 2
 0 1 3
, В  
 bo`lsa, 3А  2В ni hisoblang.
2. Agar А  
 4 0 5
 3 2 4
 1 1 2  0 1 3  3  3 6   0 2 6  3  5 0 
  2
 = 
  
  

Yechish. 3
 4 0 5   3 2 4  12 0 15   6 4 8   6  4 7 
Berilgan matritsalarni ko`paytiring:
 0 1
1 2
, В  

 2 3
3 4
1) А  
1 2
1 2
 , В  

0 1
3 4
2) A  
Berilgan matritsaga teskari matritsani toping:
1 2
,
1) А  
 2 5
 cos
2) 
 sin 
 sin  

cos 
 2 2 3


3) А   1  1 0 
  1 2 3


1 2 1


4) А   2 1 2 
 1 2 3


Uyga beriladigan topshiriqlar.
Berilgan matritsalarni ko`paytiring:
1 2
1 2
, В  

1) А  
 2 5
3 4
1 2 1
 4 1 1




2) А   2 1 2  , В    4 2 0 
 1 2 3
 1 2 1




Berilgan matritsaga teskari matritsani toping:
1 2 1


1) А   2 1 2 
 1 2 3


 1 2  3


2) А   0 1 2 
0 0 1 


а в 
,
3) А  
с
d


Quyidagi A va B matritsalarning yig’indisini hamda AB va BA matritsalarni
hisoblang
1.
2.
1 0 2 
A=  3 1 0  .
 1 1 2 


0
A=  4
2

2
1
3
0 .

1 2 
2
B=  3
1

1
0
0
4 .

1 2 
 2 0 1
B=  3 0 2  .
 1 1 2 


3.
0
A=  2
0

2
3
1  .
1
1

2
1 3
B=  2 1
0 2

 2 1 2
4. A=  3 0 2  .
1 0 1


 0 1
,
5. А  
 2 3
 cos
6. 
 sin 
0
1  .

1
 0 1 2
B=  4 0 1  .
 1 2 1 


1 2
1 2
 , С  

В  
3 4
0 1
 sin  
 1 1
 ni hisoblang. 7. 

cos 
 0 1
n
bo‘lsa, А2  2 В  5С ni hisoblang.
n
ni toping.
1  2
1 2

 ni toping. 9. 
 matritsa bilan o‘rin almashinuvchi matritsani toping.
3 4 
3 4
3
8.
1 2 1
 4 1 1




10. А   2 1 2  , В    4 2 0  bыlsa, А  В ni hisoblang.
 1 2 3
 1 2 1




2 1
 1 

 ni toping. 12. 
 ni toping.
 3  2
0 
n
11.
1 0
,
13. А  
0 4
n
 1 1

В  
 0 1
bo‘lsa, А4  В 4 ni hisoblang.
1 2 1
 4 1 1




14. А   2 1 2  , В    4 2 0  bo‘lsa, B  A ni hisoblang.
 1 2 3
 1 2 1




Minоr. Algebraik to’ldiruvchi. Ikkinchi va uchinchi tartibli determinantlar. Yuqоri tartibli
determinantlar tartibini pasaytirish usuli bilan hisoblash.
1. Berilgan matritsa rangini toping.
5 2

3 1
A
1 2

3 1

1 3

1 2
4 8

1 2 
Yechish.
5 2

3 1
1 2

3 1

1 3  -1

1 2
+
4 8

1 2 
-4
-1
+
2 1 3  1 2
5
3 
 5

 

  2  3 0 1  0  3  2 1 +


 19  6 0  4   0  6  19  4 

 

  2  3 0 1  0  3  2 1

 

-2
-1
+
5
3 
1 2


 0  3  2  1  .Demak, r(A) = 3.

0 0  15  2 


0 0
0
0 

2. Korxona 3 xil xom ashyodan foydalanib 5 xil mahsulot ishlab chiqaradi. Xom ashyo sarflash
me’yori A matritsa bilan berilgan.
 4 2 1 3 6


A   3 2 4 5 3
 2 1 5 2 4


Xom ashyoning birlik narxi B = (10 25 30) matritsa bilan berilgan. Agar ishlab chiqarish rejasi
(90, 110, 140, 180, 200) bo`lsa, korxonaning umumiy xarajatini toping.
Yechish. Avvalo ishlab chiqilgan mahsulotlar har bir turining bir birligiga ketadigan xarajatni
topamiz. Buning uchun B va A matritsalarni ko`paytiramiz:
 90 


 4 2 1 3 6
 110 


C  B  A  10 25 30   3 2 4 5 3   175 100 260 215 255 , D   140  .


 2 1 5 2 4
180




 200 


Umumiy xarajatni topish uchun C va D matritsalarni ko`paytiramiz.
 90 


 110 
X  175 100 260 215 255   140   152850


 180 
 200 

