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

^an1	2n^a ^2	^ann			^a"1	^a"2 •
^ann-1

Agar A matritsaning determinant 0 bo‘lsa u maxsus matritsa, aks holda maxsusmas matritsa deb ataladi.

m
1 2 3 4
isol. Ikkinchi tartibli determinantni hisoblang

=
1 2 3 4

О
1-4 - 2 • 3 = -

2m
2 6 - 2 1 5 4 3 -10
isol. 3-tartibli determinantni hisoblang

:

О Uchburchaklar usuli

= [2 • 5-0 + 6 • 4 • 3 + 1- (-1) • (-2)]-[(-2) • 5 • 3 + 6-1-0 + 4 • (-1) • (2)] = 112.

= (-1)¹+¹ • 2• 5 4 +(-1)'+² • 6• 1 4 +(-1)¹+³ • (-2)• 1 5 = 2-(5• 0-(-1)-4)-

О Diogcmallar usuli

- 6 -(1- 0 - 4 • 3)-2 -(1-(-1)-5 • 3) = 2 • 4 - 6-(-12)-2-(-16) = 8 + 72 + 32 = 112 3-misol. Determinantlarning xossalaridan foydalanib quyidagini isbotlang:

a	К	c + a^x+Ку		a	o^4
^a2	b2	c2 + a2x + b2y	=	^a2	^b2 ^C2
^a3	К	С + a3x + by		^a3	О CO

al

К

c++Ку

a

К

^C1

a

^b1

ajX

a

^b1

^b1 У

О

^a2

b2

c2 + a2x + ^y

=

^a2

^b2

^C2

+

^a2

^b2

a2x

+

^a2

^b2

^b2 У

^a3

bs

С + a3x + by

^a3

b3

^C3

^a3

^b3

a3x

^a3

^b3

^b3 У

= [2-5-0 + 6- 4- 3 + l- (—1) • (—2)]—[(—2) - 5- 3 + 6-1-0 + 4- (—1) • (2)] = 112.
О Birinchi и stun elementlari bo 'yichayoyib hisoblash usuli



6 5
3 -1
5 4 -1 0

4
1 0
1 4 3 0

Yuqoridagi ifodadan ko’rinadiki 2-determinantning 1-ustuni 3-ustuniga; 3-determinantda 2-ustun 3-ustunga proporsional shuning uchun ularning qiymati 0 ga teng bo’ladi. Shu bilan talab qilingan tenglik isbotlandi. •

3. 
   misol. 4-tartibli determinantni satr yoki ustun bo’yicha yoshish yordamida hisoblang.
   

- 2 - 3 0 2

1. 
   -
   A =
   12 2 3 -15 - 2 0 - 2 4 1
   

О 0 raqami qatnashgan satr yoki ustun bo’yicha yoyish berigan determinantni hisoblash qulaydir. Shuning uchun biz 1-satr bo’yicha yoyamiz:

	-1	2	2		1	2	2		1	-1	2		1	-1	2
II <	-1	5	-2	-(- 3)-	3	5	-2	+ 0 •	3	-1	-2	- 2 •	3	-1	5
	2 -	4	1		0	4	1		0	-2	1		0	-2	4

= -2 • 9 + 3 • 31 + 0 - 2 • 6 = 63

Mustaqil bajarish uchun misollar
Ikkinchi tartibli determinantlarni hisoblang va tenglamani yeching.

	cos a sin a		2x -1	x +1
1.		. 2.	x + 2	x -1
	- sin a cos a

tartibli determinantni hisoblang
1 2 3 4 5 6 7 8 9

0 1 0 2 3 4 0 5 0

4.

3.

Biror satri yoki ustuni bo’yicha yo’yish orqali 3-tartibli determinantni hisoblang

0 a 0 b c d 0 e 0

1 2 3 001 4 5 6

5.

6.

Determinantlarning xossalaridan foydalanib hisoblang
• 2 2 л
sm a cos a 1
7. sin² p cos² P 1.
22 sin у cos у 1
Determinantni satryoki ustun bo’yichayoshish yordamida hisoblang: