Chiziqli algebraik tenglamalar tizimini yechishning gauss usuli uchundastur ishlab chiqish
![cout << "a31= "; cin >> a31; cout << "a32= "; cin >> a32;
cout << "a33= "; cin >> a33; cout << "b1= "; cin >> b1;
cout << "b2= " ; cin >> b2 ; cout << "b3= "; cin >> b3;
a_22 = a12 * a21 - a22 * a11;
a_23 = a13 * a21 - a23 * a11;
a_32 = a12 * a31 - a32 * a11;
a_33 = a13 * a31 - a33 * a11;
a__33 = a_32 * a_23 - a_22 * a_33;
b_2 = b1 * a21 - b2 * a11;
b_3 = a31 * b1 - a11 * b3;
b__3 = b_2 * a_32 - b_3 * a_22;
z = (b__3) / a__33;
y = (b_2 - a_23 * z) / a_22;
x = (b1 - a13 * z - a12 * y) / a11;
cout << "x= " << x << endl;
cout << "y= " << y << endl;
cout << "z= " << z << endl;
return 0;}
#include <iostream>
#include <cmath>
using namespace std;
const int MAXN = 105;
double a[MAXN][MAXN];
double determinant(int n) {
double det = 1.0;](https://docx.uz/documents/dc116035-c013-466a-a94a-e02c620f6fd7/page_29.png?v=1)
![for (int i = 0; i < n; i++) {
int pivot = i;
for (int j = i + 1; j < n; j++) {
if (abs(a[j][i]) > abs(a[pivot][i])) {
pivot = j;
}
}
if (pivot != i) {
swap(a[i], a[pivot]);
det *= -1;
}
if (a[i][i] == 0) {
return 0;
}
det *= a[i][i];
for (int j = i + 1; j < n; j++) {
double factor = a[j][i] / a[i][i];
for (int k = i + 1; k < n; k++) {
a[j][k] -= factor * a[i][k];
}
}
}
return det;
}
int main() {
int n = 4;
double matrix[4][4] = {{1, 0, 2, -1},
{3, 0, 0, 5},
{2, 1, 4, -3},](https://docx.uz/documents/dc116035-c013-466a-a94a-e02c620f6fd7/page_30.png?v=1)
![{1, 0, 5, 0}};
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
a[i][j] = matrix[i][j];
}
}
double det = determinant(n);
cout << "Determinant = " << det << endl;
return 0;
}
III. Xulosa:
Gauss usulining xulosa ma'nosi matematikada "Gauss metodi" yoki "Gauss
eliminatsiya usuli" deb ataladi. Bu usul, liney algebra bo'yicha matritsalarni
yechish va tenglamalar sistemasini yechish uchun ishlatiladi.
Gauss usuli, matritsa ustida bir nechta qadamdan iborat ichki to'g'ri qadamli
algoritmdir. Bu usul yordamida matritsaning elementlarini o'zgartirib, matritsani
ust burchakli (ust troug'li) shaklga keltirish maqsadga muvofiq amalga oshiriladi.
Bu shaklda, matritsaning quyi burchakli elementlari 0 ga teng bo'ladi, shuningdek,
yuqori burchakdagi elementlar 1 ga teng bo'ladi.](https://docx.uz/documents/dc116035-c013-466a-a94a-e02c620f6fd7/page_31.png?v=1)
Chiziqli algebraik tenglamalar tizimini yechishning gauss usuli uchundastur ishlab chiqish