Task: Gaussian elimination
Go: package main

import (
    "errors"
    "fmt"
    "log"
    "math"
)

type testCase struct {
    a [][]float64
    b []float64
    x []float64
}

var tc = testCase{
    
    
    
    a: [][]float64{
        {1.00, 0.00, 0.00, 0.00, 0.00, 0.00},
        {1.00, 0.63, 0.39, 0.25, 0.16, 0.10},
        {1.00, 1.26, 1.58, 1.98, 2.49, 3.13},
        {1.00, 1.88, 3.55, 6.70, 12.62, 23.80},
        {1.00, 2.51, 6.32, 15.88, 39.90, 100.28},
        {1.00, 3.14, 9.87, 31.01, 97.41, 306.02}},
    b: []float64{-0.01, 0.61, 0.91, 0.99, 0.60, 0.02},
    x: []float64{-0.01, 1.602790394502114, -1.6132030599055613,
        1.2454941213714368, -0.4909897195846576, 0.065760696175232},
}


const ε = 1e-13

func main() {
    x, err := GaussPartial(tc.a, tc.b)
    if err != nil {
        log.Fatal(err)
    }
    fmt.Println(x)
    for i, xi := range x {
        if math.Abs(tc.x[i]-xi) > ε {
            log.Println("out of tolerance")
            log.Fatal("expected", tc.x)
        }
    }
}

func GaussPartial(a0 [][]float64, b0 []float64) ([]float64, error) {
    
    m := len(b0)
    a := make([][]float64, m)
    for i, ai := range a0 {
        row := make([]float64, m+1)
        copy(row, ai)
        row[m] = b0[i]
        a[i] = row
    }
    
    
    for k := range a {
        
        iMax := k
        max := math.Abs(a[k][k])
        for i := k + 1; i < m; i++ {
            if abs := math.Abs(a[i][k]); abs > max {
                iMax = i
                max = abs
            }
        }
        if a[iMax][k] == 0 {
            return nil, errors.New("singular")
        }
        
        a[k], a[iMax] = a[iMax], a[k]
        
        for i := k + 1; i < m; i++ {
            
            for j := k + 1; j <= m; j++ {
                a[i][j] -= a[k][j] * (a[i][k] / a[k][k])
            }
            
            a[i][k] = 0
        }
    }
    
    
    x := make([]float64, m)
    for i := m - 1; i >= 0; i-- {
        x[i] = a[i][m]
        for j := i + 1; j < m; j++ {
            x[i] -= a[i][j] * x[j]
        }
        x[i] /= a[i][i]
    }
    return x, nil
}

Java: import java.util.Locale;

public class GaussianElimination {
    public static double solve(double[][] a, double[][] b) {
        if (a == null || b == null || a.length == 0 || b.length == 0) {
            throw new IllegalArgumentException("Invalid dimensions");
        }
        
        int n = b.length, p = b[0].length;
        if (a.length != n || a[0].length != n) {
            throw new IllegalArgumentException("Invalid dimensions");
        }

        double det = 1.0;
        
        for (int i = 0; i < n - 1; i++) {
            int k = i;
            for (int j = i + 1; j < n; j++) {
                if (Math.abs(a[j][i]) > Math.abs(a[k][i])) {
                    k = j;
                }
            }
            
            if (k != i) {
                det = -det;
                
                for (int j = i; j < n; j++) {
                    double s = a[i][j];
                    a[i][j] = a[k][j];
                    a[k][j] = s;
                }

                for (int j = 0; j < p; j++) {
                    double s = b[i][j];
                    b[i][j] = b[k][j];
                    b[k][j] = s;
                }
            }
            
            for (int j = i + 1; j < n; j++) {
                double s = a[j][i] / a[i][i];
                for (k = i + 1; k < n; k++) {
                    a[j][k] -= s * a[i][k];
                }
                
                for (k = 0; k < p; k++) {
                    b[j][k] -= s * b[i][k];
                }
            }
        }
        
        for (int i = n - 1; i >= 0; i--) {
            for (int j = i + 1; j < n; j++) {
                double s = a[i][j];
                for (int k = 0; k < p; k++) {
                    b[i][k] -= s * b[j][k];
                }
            }
            double s = a[i][i];
            det *= s;
            for (int k = 0; k < p; k++) {
                b[i][k] /= s;
            }
        }
        
        return det;
    }
    
    public static void main(String[] args) {
        double[][] a = new double[][] {{4.0, 1.0, 0.0, 0.0, 0.0},
                                       {1.0, 4.0, 1.0, 0.0, 0.0},
                                       {0.0, 1.0, 4.0, 1.0, 0.0},
                                       {0.0, 0.0, 1.0, 4.0, 1.0},
                                       {0.0, 0.0, 0.0, 1.0, 4.0}};

        double[][] b = new double[][] {{1.0 / 2.0},
                                       {2.0 / 3.0},
                                       {3.0 / 4.0},
                                       {4.0 / 5.0},
                                       {5.0 / 6.0}};
                                       
        double[] x = {39.0 / 400.0,
                      11.0 / 100.0,
                      31.0 / 240.0,
                      37.0 / 300.0,
                      71.0 / 400.0};
                                       
        System.out.println("det: " + solve(a, b));
        

        for (int i = 0; i < 5; i++) {
            System.out.printf(Locale.US, "%12.8f %12.4e\n", b[i][0], b[i][0] - x[i]);
        }
    }
}