# Untitled

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```#include <stdio.h>

int main() {
float x[10], y[10], a[3][4];
int n, i, j, k;

printf("Enter number of data points: ");
scanf("%d", &n);

printf("Enter data points x[i], y[i]: \n");
for (i = 0; i < n; i++) {
scanf("%f %f", &x[i], &y[i]);
}

// Calculate sums
float sum_x = 0, sum_y = 0, sum_xy = 0, sum_x2 = 0, sum_x3 = 0, sum_x4 = 0, sum_x2y = 0;
for (i = 0; i < n; i++) {
sum_x += x[i];
sum_y += y[i];
sum_xy += x[i] * y[i];
sum_x2 += x[i] * x[i];
sum_x3 += x[i] * x[i] * x[i];
sum_x2y += x[i] * x[i] * y[i];
sum_x4 += x[i] * x[i] * x[i] * x[i];
}

// Fill matrix
a[0][0] = n;
a[0][1] = a[1][0] = sum_x;
a[0][2] = a[1][1] = a[2][0] = sum_x2;
a[0][3] = sum_y;
a[1][2] = a[2][1] = sum_x3;
a[1][3] = sum_xy;
a[2][2] = sum_x4;
a[2][3] = sum_x2y;

// Print matrix
printf("\nThe matrix is:\n");
for (i = 0; i < 3; i++) {
for (j = 0; j <= 3; j++)
printf("%.2f\t", a[i][j]);
printf("\n");
}

// Gauss elimination
for (i = 0; i < 2; i++) {
for (k = i + 1; k < 3; k++) {
double t = a[k][i] / a[i][i];
for (j = 0; j <= 3; j++)
a[k][j] = a[k][j] - t * a[i][j];
}
}

// Print matrix after Gauss elimination
printf("\n\nThe matrix after gauss-elimination is as follows:\n");
for (i = 0; i < 3; i++) {
for (j = 0; j <= 3; j++)
printf("%.2f\t", a[i][j]);
printf("\n");
}

// Back-substitution
float x_vals[3];
for (i = 2; i >= 0; i--) {
x_vals[i] = a[i][3];
for (j = i + 1; j < 3; j++) {
if (j != i)
x_vals[i] -= a[i][j] * x_vals[j];
}
x_vals[i] /= a[i][i];
}

// Print values of variables
printf("\nThe values of the variables are as follows:\n");
for (i = 0; i < 3; i++)
printf("%.2f\n", x_vals[i]);

return 0;
}
```