Explain the following code:

public class GaussianElimination {

public static void main(String[] args) {

double[][] A = {{2, 1, -1}, {-3, -1, 2}, {-2, 1, 2}}; // coefficient matrix

double[] b = {8, -11, -3}; // constant vector

int n = b.length;

// forward elimination

for (int k = 0; k < n-1; k++) {

for (int i = k+1; i < n; i++) {

double factor = A[i][k] / A[k][k];

for (int j = k+1; j < n; j++) {

A[i][j] -= factor * A[k][j];

}

b[i] -= factor * b[k];

}

}

// backward substitution

double[] x = new double[n];

x[n-1] = b[n-1] / A[n-1][n-1];

for (int i = n-2; i >= 0; i--) {

double sum = b[i];

for (int j = i+1; j < n; j++) {

sum -= A[i][j] * x[j];

}

x[i] = sum / A[i][i];

}

// print solution

System.out.println("Solution:");

for (int i = 0; i < n; i++) {

System.out.println("x[" + i + "] = " + x[i]);

}

}

}