Reja: Kirish. 1.Chiziqli tenglamalar sistemasini Gauss usulida hisoblash 2.Chiziqli tenglamalar sistemasini Kramer usulida hisoblash 3.Matritsa tenglamasini teskari matritsa toppish usulida hisoblash Xulosa . Foydalanilgan adabiyotlar.

1. CHIZI Q LI TENGLAMALAR SISTEMACINI Y ECHISH Chiziqli tenglamalar sistemasini Gauss, Kramer va teskari matritsa usullari bilan y echimini topish masala la rini ko‘ramiz. 1.1-masala. Quyidagi uch noma’lumli chiziqli tenglamalar sistemasi ning yechimini: 1) Gauss usuli, 2) Kramer, 3) Matritsa usulida toping.             39 16 25 5 18 12 14 3 0 13 7 2 3 2 1 3 2 1 3 2 1 x x x x x x x x x (1) 1.1. Gauss usulida y echish. Yetakchi tenglama uchun birinchi tenglamani olamiz. Bu tenglamadan etakchi noma’lum uchun x 1 va a 11 ≠0 ni etakchi element uchun tanlaymiz. Birinchi tenglama dagi x 1 ning koeffitsenti a 11 ni 1 ga aylantirish uchun birinchi tenglamani ng barcha qo‘shiluvchilarini a 11 ≠0 ga b o‘ lamiz . Ҳosil bo‘lgan tenglamadan foydalanib ikkinchi va uchinchi tenglmalardan x 1 nomahlumni yo‘qotish yoki uning koeffitsentini nolg‘ga aylantirish uchun etakchi tenglamani –3 ga ko‘paytirib 2- tenglamaga qo‘shamiz, so‘ngra etakchi tenglamani –5 ko‘paytirib 3- teglamaga qo‘shamiz. Natijada quyidagicha sistemaga kelamiz:                39 2 33 2 15 18 2 15 2 7 0 13 7 2 3 2 3 2 3 2 1 x x x x x x x Bu tenglamlar sistemasida etakchi tenglama uchu 2- tenglamani olamiz. Unda 7/2 koeffitsient l i x 2                7 3 7 3 18 2 15 2 7 0 13 7 2 332 321 x x x x x x bu sistemaning 3- tenglamasidan x 3 nomahlumni topamiz. x 3 asosida 2- tenglamadan x 2 ni topamiz. x 3 , x 2 lar asosida 1- tenglamadan x 1 ni topamiz. x 3 = - 1 x 2 = 3 )2 15 18(7 2 ) 2 15 18(7 2 3     x x 1 = 4 ))1 ( 13 3 7( 2 1 ) 13 7( 2 1 3 2         x x Demak sistema echimi: x 1 =-4, x 2 =3, x 3 = -1

Maple12 dasturida masalani echish. Uch noma’lumli chiziqli tenglamalar sistemasini oddiy va Gauss usulida echish( 1 . 1 - masala). 1 2 3 1 2 3 1 2 32 7 13 0, 3 14 12 18, 5 25 16 39, ő ő ő ő ő ő ő ő ő               Maple7 dasturida masalalarni echishdagi amallarni bajarish uchun ishchi oynada > belgidan so‘ng kerakli buyruqni yozib Enter tugmasini bosish kerak. 1. Oddiy usulida echish ( Gauss.mw ). > solve( {2*x + 7*y + 13*z = 0, 3*x + 14*y + 12*z =18, 5*x + 25*y +16*z =39}, [x, y, z]); [x=-4, y=3, z=-1] 2. Gauss usulida uch noma’lumli chiziqli tenglamalar sistemasini echish . > with(LinearAlgebra): A := <<2,3,5>|<7,14,25>|<13,12,16>>; 2 7 13 : 3 14 12 5 25 16 A         > B := <0,18,39>; 0 : 18 39 b         > GaussianElimination(A); 2 7 13 7 15 0 3 2 3 0 0 7              > GaussianElimination(A,'method'='FractionFree'); 2 7 13 0 7 15 0 0 3             >ReducedRowEchelonForm(<A|b>); 1 0 0 4 0 1 0 3 0 0 1 1            

3. To‘rt noma’lumli chiziqli tenglamalar sistemasini Maple12 dasturida echish 1) Oddiy usulida echish > sys:=({1*x1-5*x2-1*x3+3*x4=-5,2*x1+3*x2+1*x3-1*x4=4, 3*x1-2*x2+3*x3+4*x4=- 1,5*x1+3*x2+2*x3+2*x4=0}): > solve(sys,{x1,x2,x3,x4});{x4 = K 3,x2 = K 1,x1 = 1,x3 = 2} 2) Gauss usulida echish       0.= 2x+ 2x+ 3x+ 5x -1,= 4x+ 3x+ 2x- 3x 4,= x- x3+ 3x+ 2x -5,= 3x+ x- 5x- x 4 3 2 1 4 3 2 1 4 2 1 4 3 2 1 > with(LinearAlgebra): A := <<1,2,3,5>|<-5,3,-2,3>|<-1,1,3,2>|<3,-1,4,2>>; 1 5 1 3 2 3 1 1 : 3 2 3 4 5 3 2 2A                  > b := <-5,4,-1,0>; 5 4 : 1 0 B             > GaussianElimination(A,'method'='FractionFree');                39/ 67 0 0 0 2 3 0 0 7 3 13 0 3 1 5 1 > ReducedRowEchelonForm(<A|b>);               3 0 0 0 2 1 0 0 1 0 1 0 1 0 0 1

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