Matrix LU C#

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Globalization;

namespace Matrix
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("введите название файла *data#.txt*");
            int NumbX = 0;
            var userInput = Console.ReadLine();
            var data = File.ReadAllLines(userInput);
            var numberOfur = int.Parse(data[0]);
            var mathrix = new double[numberOfur, numberOfur];
            var sqrs = new double[numberOfur];
            InitialiseData(mathrix, sqrs, data, numberOfur);
            var determinant = CalculateDeterminat(mathrix, sqrs);
            var answers = CalculateAnswers(mathrix, sqrs, determinant);
            foreach (var a in answers)
            {
                Console.WriteLine($"X{NumbX} == {a}");
                NumbX++;
            }

            Console.ReadKey();

        }

        private static void InitialiseData(double[,] matrix, double[] sqrs, string[] data, int numberOfur)
        {
            for (int i = 1; i < numberOfur + 1; i++)
            {
                var dataInLine = data[i].Split().Select(x => double.Parse(x, CultureInfo.InvariantCulture)).ToArray();
                for (int j = 0; j < numberOfur; j++)
                {
                    matrix[i - 1, j] = dataInLine[j];
                }
                sqrs[i - 1] = dataInLine[numberOfur];
            }
        }

        private static double[] CalculateAnswers(double[,] mathrix, double[] sqrs, double determinant)
        {
            var answers = new double[sqrs.Length];
            for (int i = 0; i < sqrs.Length; i++)
            {
                var cahce = new double[sqrs.Length];
                for (int j = 0; j < sqrs.Length; j++)
                {
                    cahce[j] = mathrix[j, i];
                    mathrix[j, i] = sqrs[j];
                }
                var matrix = new double[sqrs.Length, sqrs.Length];
                for (int a = 0; a < sqrs.Length; a++)
                    for (int b = 0; b < sqrs.Length; b++)
                        matrix[a, b] = mathrix[a, b];
                answers[i] = CalculateDeterminat(matrix, new double[sqrs.Length]) / determinant;
                for (int j = 0; j < sqrs.Length; j++)
                {
                    mathrix[j, i] = cahce[j];
                }
            }
            return answers;
        }

        private static double CalculateDeterminat(double[,] matrix, double[] sqrs)
        {
            var determinant = matrix[0, 0];
            var index = 0;
            while (index < sqrs.Length - 1)
            {
                for (int i = index; i < sqrs.Length - 1; i++)
                {
                    var delitel = matrix[i + 1, index] / matrix[index, index];
                    for (int j = 0; j < sqrs.Length; j++)
                    {
                        matrix[i + 1, j] -= matrix[index, j] * delitel;

                    }
                    sqrs[i + 1] -= sqrs[index] * delitel;
                }
                index++;
                determinant *= matrix[index, index];

            }
            return determinant;
        }
    }
}