Mavzu. Matritsa va aniqlovchilar matritsalar ustida amallar: qo’shish, ayirish, songa ko’paytirish va ko’paytirish. Eslatma

1. 
   mavzu. MATRITSA VA ANIQLOVCHILAR
   

Matritsalar ustida amallar: qo’shish, ayirish, songa ko’paytirish va ko’paytirish. Eslatma.Ikkita matritsani qo’shish yoki ayirish uchun bu matritsalarning tartibi bir xil bo’lishi shart

.

(1 2

3 "

(- 2 3 0"

( 2

4

6 "

(- 6 9

0 "

(2 - 6

4 + 9 6 + 0 "

2 A + 3B = 2 •

+ 3 •

=

+

=

v^0 1

- ^1j

v ^211J

v ^0

2

^- 2 J

3 6

^3 J

v 0 + 6

2 + 3 - 2 + 3y

л f
va B =

J

V

bo’lsa, 2A + 3B ning chiziqli kombinatsiyasini toping.

^r- 4 13 6^Л 6 5 1

2 3 1 -1

- 2 3 2 1

1-misol. Agar A =

(3	1 "		( 6 - 4 "
0	- 2	, B =	1 2
, 4	5 .		V J

2-misol. Agar A =

bo’lsa, AB va BA hisoblang.

О A_3x2 • B_2x2 ni hisoblaymiz. Ushbu matritsalarda m=3, p=q=2, n = 2 bo‘lgani uchun ularning ko‘paytirish

mumkin va ko‘paytma matritsa AB = C_3x2 quyidagicha bo‘ladi:

3 • (-4) +1-2 "
0 • 6 + (-2)-1 0 • (-4) + (-2) • 2 _{v y v} 4 • 6 + 5 4 4 • (-4) + 5 • 2 _y
B_2X2 • A_3x2 ni hisoblaymiz. Bunda B matritsada m = 2,p = 2 va A matritsada q=3, n=2. BA ko’paytma o’rinli bo’lishi uchunp=q bo’lishi kerak edi, lekin p Ф q bundan ko’rinadiki ko’paytma o’rinli emas. Masalan
(3 1 "

( 3

(19 -10" -2 -4 29 -6

A • B =

0 - 2 4 5

12

(6 • 3 - 4 • 0 + ?• 4 6 4 - 4 •(- 2)+ ?• 5" 13 + 2 • 0 + ?• 4 14 + 2 •(- 2)+?• 5

. Ya’ni B • A mavjud emas.

B • A =
^B2x2 ^a3x2

0 - 2 4 5

v ^{1 2} J

у

V

1 2 3 0

3-misol. Agar A =

bo’lsa, A ni hisoblang.
^14 + 2 • 3 12 + 2 • 0" 3 4 + 0 • 3 3 • 2 + 0 • 0

V'

1 2 " 30

О A² = A • A =

	( 2	-1	2 "		( 2	-1	0 "		( 3	1 2 "
ll 9' - 1.	5	3 -	3	ll ocT no - ■'t 2.	3	4	- 2	, B =	- 2	1 3
	V-^1	0	^- 2 J		v- ^3	1	^5 J		v ^0	■'t - 2

J

V~

J

Mustaqil bajarish uchun misollar
Berilgan matritsalarning chiziqli kombinatsiyalarini toping:

AB va BA matritsalar ko’paytmasini hisoblang (agar ular mavjud bo’lsa):

	( 2	0	1 "		(- 3	1 0"		(1	3 "		(1	- 2 3"
3. А =	- 2	3	2	, В =	0	2 1	4. А =	2	0	, В =	5	4 0,
	V ^4	-1	^5 J		v ^0	-1 3J		V ^1	- ^1J		V	^J