Referat mavzu. Matritsa ustida almashtirishlar toshkent 2016

3. Mashqlar

3.1. Agar A matritsa nosingular va simmetrik bo‘lsa, A^1 matritsa ham nosingular va simmetrik bo‘lishini ko‘rsating,
3.2. Agar A kvadrat matritsa va (I  A) nosingular matritsa bo‘lsa,
A(I A)^1 (I A)^1A tenglik bajarilishini ko‘rsating.
a c
3.3. A_b d_ matritsaning teskari matritsaga ega bo‘lishi shartini toping.
_

 2 3.4. A3 	5   7	7 5 va C^  bo‘lsin. CA^^1 ekanini ko‘rsating.
		3 2  
 4  3.5. B18  3  ko‘rsating.	0 1 0	5 4 0   24 matritsa A0 1 4 3 0 	5  6 matritsaning teskari matritsasi bo‘lishini 4
 1 	11	3 5 3   21 11 matritsa A 4	2  1 matritsaning teskari matritsasi
3.6. B  17

    
36 10 6 2 3 1 5    bo‘lishini ko‘rsating. 3.7. Berilgan matritsalardan qaysi birlari uchun teskari matritsa mavjud bo‘ladi?
1 2 0  1 3 9 0 5    1) A2 6; 2) B7 2; 3) C ^3^25^2116 ^; D^02   0 1 3.8. A^1 1 bo‘lsin. A^2A^^1 va A^3I bo‘lishini ko‘rsating. 3.9. Berilgan matritsalardan qaysi birlari o‘zaro teskari matritsalar bo‘ladi?				2 1 3		1  3. 10
1 1 0 1 3 5  2 5 1) ^ 1  va ^1 1^; 2) ^1 2^ va 1 3; 0
1 2 0  7 3 0 15 0    ^0 5 va 50 3; 4) ^10 ^23 13^ va ^^23  3 6 A^ 2 5 matritsa berilgan. A^^1 matritsani toping.   5 2 A . matritsa berilgan. A^^1matritsani toping. 1 4 Berilgan shartlarni qanoatlantiruvchi A matritsani toping: 1 1 1 1 1 1) (3A)^^1^0 1; 2) (2A)^T^2 3 ;  0 1 2 3) (AT 2I)1 21 10; 4) A1 14 03 83 .  	2 1 1	6  3 . 2

 1 0 0
 

3.13. ABC 5 1 0 bo‘lsin. C^1B^1A^1 ni toping.
 0 0 1
3 2 3
 
3.14. A 4 1 6 matritsa berilgan. C  AadjA ko‘paytmaning barcha nodiagonal
 7 5 1
elementlarini toping.
1 2 3
 
3.15. A0 2 4_ matritsa berilgan. C  AadjA ko‘paytmaning barcha diagonal
1 3 0
elementlarini toping.
A matritsa berilgan. A^1 matritsani toping:
1 1 1 1 2 3
   
3.16. A1 2 1. 3.17. A2 6 4.
2 2 4 3 10 8

A matritsa berilgan. A^1 matritsani Jordan-Gauss usuli bilan toping:
 1 0 1 2  1 1 0 1
   
_ 2 1 0 1 1 0 1 0
3.18. A _{1 1 2 1}. 3.19. A _{2 1 1 2}.
   
^1 1 2 1^_ _ 0 1 2 0_
3.20. A matritsa berilgan. Matritsaning LU yoyilmasini toping:
2 1  6 4

8 7 12			5
 3  3) A9  9 	1 0 9	2  2   4; 4) A 4 14  6	3 13 5	2  9; 4
 2  5) A ^ 6  4 	0 3 6	 2  5 2^ 4 13 3^; 6) A  ^ 6  16 17   6    8 	3 8 5 9 6	4  7 14 ^. 12  10  

1) A_ _; 2) A_ _;
A matritsa berilgan. r(A)ni minorlar ajratish usuli bilan toping:
 1 1 2 3  1 2 3
   
3.21. A1 3 0 1. 3.22. A1 4 2.
 3 4 1 1  2 2 7 
A matritsa berilgan. r(A)ni elementar almashtirishlar usuli bilan toping:
1 1 3 4
 1 3 2 1  
3.23. A23 11 46 116. 3.24. A^_₁12 _^1₄3 0₃^{3 }₁9^2_.
Adabiyotlar

1. 
   Yo.U.Soatov. Oliy matematika 1-tom., T, “O’qituvchi” 1992
   
2. 
   Yo.U.Soatov. Oliy matematika 2-tom., T, “O’qituvchi” 1992
   
3. 
   Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162169.
   
4. 
   Kenneth L. Kuttler-Elementary Linear Algebra [Lecture notes] (2015). pp.
   

96-99.

5. 
   Sh.R.Xurramov ”Matematika” Toshkent- 2016.
   

1^ E.Kreyszig. Advancet engineering Matematics. Copyright. 2011, pp. 267-268

2^ Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169

3^ Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169

4^ Kenneth L. Kuttler-Elementary Linear Algebra [Lecture notes] (2015). pp. 96-99

5^ Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169

6^ Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169

7^ Kenneth L. Kuttler-Elementary Linear Algebra [Lecture notes] (2015). pp. 96-99

8^ ~ ^_ 00 00 00 4 105^_~ _0000 00 02 15 _U. _

2

Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169

9^ Kenneth L. Kuttler-Elementary Linear Algebra [Lecture notes] (2015). pp. 96-99

10^ Lay, David C. Linear algebra and is applications. Copyright. 2012, pp.162-169