Task: Cramer's rule
Go: package main

import (
    "fmt"

    "gonum.org/v1/gonum/mat"
)

var m = mat.NewDense(4, 4, []float64{
    2, -1, 5, 1,
    3, 2, 2, -6,
    1, 3, 3, -1,
    5, -2, -3, 3,
})

var v = []float64{-3, -32, -47, 49}

func main() {
    x := make([]float64, len(v))
    b := make([]float64, len(v))
    d := mat.Det(m)
    for c := range v {
        mat.Col(b, c, m)
        m.SetCol(c, v)
        x[c] = mat.Det(m) / d
        m.SetCol(c, b)
    }
    fmt.Println(x)
}

Java: import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class CramersRule {

    public static void main(String[] args) {
        Matrix mat = new Matrix(Arrays.asList(2d, -1d, 5d, 1d), 
                                Arrays.asList(3d, 2d, 2d, -6d), 
                                Arrays.asList(1d, 3d, 3d, -1d),
                                Arrays.asList(5d, -2d, -3d, 3d));
        List<Double> b = Arrays.asList(-3d, -32d, -47d, 49d);
        System.out.println("Solution = " + cramersRule(mat, b));
    }
    
    private static List<Double> cramersRule(Matrix matrix, List<Double> b) {
        double denominator = matrix.determinant();
        List<Double> result = new ArrayList<>();
        for ( int i = 0 ; i < b.size() ; i++ ) {
            result.add(matrix.replaceColumn(b, i).determinant() / denominator);
        }
        return result;
    }
        
    private static class Matrix {
        
        private List<List<Double>> matrix;
        
        @Override
        public String toString() {
            return matrix.toString();
        }
        
        @SafeVarargs
        public Matrix(List<Double> ... lists) {
            matrix = new ArrayList<>();
            for ( List<Double> list : lists) {
                matrix.add(list);
            }
        }
        
        public Matrix(List<List<Double>> mat) {
            matrix = mat;
        }
        
        public double determinant() {
            if ( matrix.size() == 1 ) {
                return get(0, 0);
            }
            if ( matrix.size() == 2 ) {
                return get(0, 0) * get(1, 1) - get(0, 1) * get(1, 0);
            }
            double sum = 0;
            double sign = 1;
            for ( int i = 0 ; i < matrix.size() ; i++ ) {
                sum += sign * get(0, i) * coFactor(0, i).determinant();
                sign *= -1;
            }
            return sum;
        }
        
        private Matrix coFactor(int row, int col) {
            List<List<Double>> mat = new ArrayList<>();
            for ( int i = 0 ; i < matrix.size() ; i++ ) {
                if ( i == row ) {
                    continue;
                }
                List<Double> list = new ArrayList<>();
                for ( int j = 0 ; j < matrix.size() ; j++ ) {
                    if ( j == col ) {
                        continue;
                    }
                    list.add(get(i, j));
                }
                mat.add(list);
            }
            return new Matrix(mat);
        }

        private Matrix replaceColumn(List<Double> b, int column) {
            List<List<Double>> mat = new ArrayList<>();
            for ( int row = 0 ; row < matrix.size() ; row++ ) {
                List<Double> list = new ArrayList<>();
                for ( int col = 0 ; col < matrix.size() ; col++ ) {
                    double value = get(row, col);
                    if ( col == column ) {
                        value = b.get(row);
                    }
                    list.add(value);
                }
                mat.add(list);
            }
            return new Matrix(mat);
        }

        private double get(int row, int col) {
            return matrix.get(row).get(col);
        }
        
    }

}