chiziqli almashtirishlar va ularning matritsasi

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chiziqli almashtirishlar va ularning matritsasi biror bazisda berilgan ixtiyoriy 1 2 3( , , )x x x x vektorni  almashtirish quyidagi vektorga o’tkazadi: 1 2 2 1 2 3( , 2 , )x x x x x x x     . ushbu almashtirish chiziqli bo’ladimi? agar  chiziqli almashtirish bo’lsa, uning matritsasini toping. yechish: chiziqli fazodan ixtiyoriy ikkita 1 2 3( , , )x x x x va 1 2 3( , , )y y y y vektorlarni olaylik. u holda 1 1 2 2 3 3 1 2 1 2 2 2 1 2 3 1 2 3 ( ) [( , , )] ( , 2 2 , ) ( ) ( ). x y x y x y x y x x y y x y x x x y y y x y          …

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,0,1), (1,1,0), (0,1,1), (1,1,1), (1,0, 1), (0,1,2);a a a b b b       ;  1 2 3 1 2 3( 2,3,0), (0,3,2), (4,0,0), (1,2,1), ( 1,1, 1), (2, 1,2);a a a b b b          ;  1 2 3 1 2 3(1,0,0), (0,1,0), (0,0,1), (0,0,1), (0,1,0), (1,0,0);a a a b b b      ;  1 2 3 1 2 3(2,0,1), ( 1,1,2), (1,1,9), (8,9,1), (1,1,0), (2,9,2);a a a b b b       1-misol. a almashtirish r chiziqli fazoda 0ax x x  tenglik bilan aniqlangan, bu yerda 0x r fiksirlangan noldan farqli vektor. a chiziqli almashtirish bo’ladimi? yechilishi: chiziqli almashtirish ta’rifiga ko’ra quyidagi ikkita shartni tekshiramiz: 0ax x x  , 0ay y x  ,   0a x y x y x  …

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x x y z y x y z z x y z b x x y z y x y z z x y z                       yechilishi.  1 2 3, ,e e e bazisda birinchi va ikkinchi almashtirishlarning mos ravishda matrissalari 1 2 3 4 5 6 7 8 9 a            va 1 3 4.5 6 7 9 10.5 12 13 b            . u holda 1 2 3 1 3 4.5 1 0 0 3 2 3 4 5 6 2 6 7 9 0 1 0 7 8 9 10.5 12 13 0 0 1 a b         …

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                                                               demak 3 2 1 1 2 3 4 3 0 3 2 0 0 2 3 6 b                  .   chiziqli almashtirishning 1 2 3 4, , ,e e e e bazisdagi matritsasi 1 2 0 1 3 0 1 2 2 5 3 1 1 2 1 3             bo’lsa, u holda ushbu chiziqli chiziqli almashtirishning quyidagi …

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chiziqli almashtirishlar va ularning matritsasi biror bazisda berilgan ixtiyoriy 1 2 3( , , )x x x x vektorni  almashtirish quyidagi vektorga o’tkazadi: 1 2 2 1 2 3( , 2 , )x x x x x x x     . ushbu almashtirish chiziqli bo’ladimi? agar  chiziqli almashtirish bo’lsa, uning matritsasini toping. yechish: chiziqli fazodan ixtiyoriy ikkita 1 2 3( , , )x x x x va 1 2 3( , , )y y y y vektorlarni olaylik. u holda 1 1 2 2 3 3 1 2 1 2 2 2 1 2 3 1 2 3 ( ) [( , , )] ( , 2 2 , ) ( ) ( ). x …

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