Chiziqli tenglamalar sisitemasini yechish

Demak sistema echimi: x₁=-4, x₂=3, x₃= -1

Maple7 dasturida masalani echish.
Uch noma’lumli chiziqli tenglamalar sistemasini oddiy va Gauss usulida echish(1.1- masala).

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>>;

> B := <0,18,39>;

> GaussianElimination(A);

> GaussianElimination(A,'method'='FractionFree');

>ReducedRowEchelonForm();

3. To‘rt noma’lumli chiziqli tenglamalar sistemasini Maple7 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});

2) Gauss usulida echish

> with(LinearAlgebra):
A := <<1,2,3,5>|<-5,3,-2,3>|<-1,1,3,2>|<3,-1,4,2>>;



> b := <-5,4,-1,0>;

> GaussianElimination(A,'method'='FractionFree');



> ReducedRowEchelonForm();



1.2. Kramer qoidasi yordamida echish.

Berilgan tenglamalar sistema nomahlumlarning koeffitsientlari va ozod hadalari yordamida determinantlarni tuzamiz va ularni hisoblashning uchburchak yoki Sarrus usullaridan foydalanamiz. Biz (1) tenglamlar sistemasining determinantlarini tuzib, uchburchak usulida hisolab uni son qiymatlarni topamiz.

₃ =