matritsalarning amallari

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1.1 asosiy nazariy materiallar 1-ma’ruza matritsalar nazariyasi elementlari: asosiy ta’rif va tushunchalar. matritsalarning turlari. matritsalarni songa ko’paytirish, matritsalarni qo’shish, matiritsalarni ayirish va matritsani matritsaga ko’paytirish amallari, hamda ularning xossalari. reja 1. matritsa tushunchasi 2. matritsalar ustida amallar ( m )2.1-tahrif. n matritsa tushunchasi sonlarning to’g’ri to’rtburchakli jadvaliga m ta satr va n ta ustunli m n o’lchovli matritsa deyiladi. ( a 11 a 1 n . . . . a m 1 a mn )a a matritsada i –satr (ai1 . . . ain ) va j -ustun ko’rinishida bo’ladi. 2.1. ( a 1 j . . a mj )-misol 3 4 o’lchovli matritsani ko’raylik. ( 1 2 6 ) ( 2 3 1 )1 3 a 1 5 0 7 bu matritsada (3 1 5 2) 3 2- satrni va 5 7 3- ustunini bildiradi. 2.2 . matritsalar ustida amallar m n o’lchovli a va b matritsalar berilgan bo’lsin. …

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atritsa bo’lsin. u holda quyidagilar o’rinli: 1) с 2) (c ( а b) d ) a a c b ( с ) ( с )a d a 3) 0 а 0 4) c (dа) (c d ) a ( . )matritsalar ko’paytmasini aniqlash uchun, avval chiziqli tenglamalar sistemasini ko’rib chiqamiz. a11 x1 . . a1n xn b1 ( . ). . . . . . . . . . . . . . . . . . (1) am1 x1 . . amn xn bm bu sistemani matritsalar ko’rinishida yozadigan bo’lsak, аx ( b )(*) bo’ladi, bu yerda, a11 . . . . . . . a1n . x1 . b1 . a . . (2), x . (3), в . (4) . . . . an1 . . . . . . ann bn ( x n )bo’lib , (*) yozuvni a11 . . . . . . a1n …

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ovli matritsalar. 4) c ( ab) (ca) b a(cb), bu yerda a m n o’lchovli, b n p o’lchovli matritsalar с haqiqiy son. endi chiziqli tenglamalar sistemasini o’rganamiz. bizga (1) ko’rinishdagi chiziqli tenglamalar sistemasi berilgan bo’lsin. bu sistemaning matritsa ko’rinishida yozuvi аx ega. b bo’lib, а, x, b matritsalar (2), (3), (4) ko’rinishga 2.13-teorema. har qanday (1) ko’rinishdagi sistema yoki echimga ega emas, yoki bitta echimga ega, yoki cheksiz ko’p echimga ega bo’ladi. bu bo’limda kvadratik matritsalar bilan ishlaymiz. ( a 11 a 1 n . . . . . , a ij . 1 i j 0 i j a n 1 a nn )2.14-tahrif. n n olchovli kvadratik matritsa i n ( 1 , i 4 ) ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 )n tartibli birlik matritsa deyiladi. masalan: i1 2.15- xossa. ( n )n o’lchovli а …

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ay bo’ladi? 16. qanday matritsalarni ko’paytirish mumkin? 17. matritsalar qanday ko’paytiriladi? 18. elementar almashtirishlar deb qanday amallarga aytiladi? image6.png image96.png image97.png image98.png image99.png image100.png image101.png image102.png image103.png image104.png image105.png image7.png image106.png image107.png image108.png image109.png image110.png image111.png image112.png image113.png image114.png image115.png image8.png image116.png image117.png image118.png image119.png image120.png image121.png image122.png image123.png image124.png image125.png image9.png image126.png image127.png image128.png image129.png image130.png image131.png image132.png image133.png image134.png image135.png image10.png image136.png image137.png image138.png image139.png image140.png image141.png image142.png image143.png image144.png image145.png image11.png image146.png image147.png image148.png image149.png image12.png image13.png image14.png image15.png image16.png image17.png image18.png image19.png image20.png image21.png image22.png image23.png image24.png image25.png image26.png image27.png image28.png image29.png image30.png image31.png image32.png image33.png image34.png image35.png image36.png image37.png image38.png image39.png image40.png image41.png image42.png image43.png image44.png image45.png image1.png image46.png image47.png image48.png image49.png image50.png image51.png image52.png image53.png image54.png image55.png image2.png image56.png image57.png image58.png image59.png image60.png image61.png image62.png image63.png image64.png image65.png image3.png image66.png image67.png image68.png image69.png image70.png image71.png image72.png image73.png image74.png image75.png image4.png image76.png image77.png image78.png image79.png …

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siy nazariy materiallar 1 - ma’ruza matritsalar nazariyasi elementlari: asosiy ta’rif va tushunchalar. matritsalarning turlari. matritsalarni songa ko’paytirish, matritsalarni qo’shish, matiritsalarni ayirish va matritsani matritsaga ko’paytirish amallari, hamda ularning xossalari. reja 1. matritsa tushunchasi 2. matritsalar ustida amallar 2.1 - tahrif. n matritsa tushunchasi sonlarning to’g’ri to’rtburchakli jadvaliga m ta satr va n ta ustunli m n o’lchovli matritsa deyiladi. a a matritsada i – satr ( a i 1 . . . a in ) va j - ustun ko’rinishida bo’ladi. 2.1. - misol 3 4 o’lchovli matritsani ko’raylik. 1 3 a 1 5 0 7 bu matritsada (3 1 5 2) 3 2 - satrni va 5 7 3 - ustunini bildiradi. 2.2 . matritsalar ustida amallar m n o’lchovli a va b matritsalar berilgan bo’lsin. 2.3 - tahrif. m a 11 ........................ a 1 n . . . . a m 1 ....................... a mn a 1 …

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1.1 asosiy nazariy materiallar 1-ma’ruza matritsalar nazariyasi elementlari: asosiy ta’rif va tushunchalar. matritsalarning turlari. matritsalarni songa ko’paytirish, matritsalarni qo’shish, matiritsalarni ayirish va matritsani matritsaga ko’paytirish amallari, hamda ularning xossalari. reja 1. matritsa tushunchasi 2. matritsalar ustida amallar ( m )2.1-tahrif. n matritsa tushunchasi sonlarning to’g’ri to’rtburchakli jadvaliga m ta satr va n ta ustunli m n o’lchovli matritsa deyiladi. ( a 11 a 1 n . . . . a m 1 a mn )a a matritsada i –satr (ai1 . . . ain ) va j -ustun ko’rinishida bo’ladi. 2.1. ( a 1 j . . a mj )-misol 3 4 o’lchovli matritsani ko’raylik. ( 1 2 6 ) ( 2 3 1 )1 3 a 1 5 0 …

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