在行列式消元中的判断条件有问题，这里给出订正后的代码：

1）MyMathLib.LinearAlgebra.CalcDeterminant方法

/// <summary>
        /// 化三角法行列式计算,
        /// </summary>
        /// <param name="Determinants">N阶行列式</param>
        /// <returns>计算结果</returns>
        public static double CalcDeterminant(double[,] Determinants)
        {
            int theSign = 1;//正负符号，如果需要变换，将记录变换后的符号.
            int theN = Determinants.GetLength(0);
            //从第1列到第theN-1列
            for (int i = 0; i < theN - 1; i++)
            {
                //从第theN-1行到第i+1行，将D[j,i]依次变为0
                for (int j = theN - 1; j > i; j--)
                {
                    //如果为当前值为0，则不处理,继续处理上一行
                    if (Determinants[j, i] == 0)
                    {
                        continue;
                    }
                    //修订部分：
                    //如果左上邻元素[j-1, i-1]以及其左边的元素都为0方可交换
                    //因为当前元素的左边元素已经全部是零，因此如果要交换不能使本行左边产生非零数，
                    //则需要左上邻及其所有元素皆为0.
                    var theCanDo = true;
                    for (int s = i - 1; s >= 0; s--)
                    {
                        if (Determinants[j - 1, s] != 0)
                        {
                            theCanDo = false;
                            break;
                        }
                    }
                    if (theCanDo)
                    {
                        //如果[j,i]的上一行[j-1, i]的值为0则交换
                        if (Determinants[j - 1, i] == 0)
                        {
                            //每次交换，行列式的值大小不变，符号取反
                            theSign = 0 - theSign;
                            for (int k = 0; k < theN; k++)
                            {
                                double theTmpDec = Determinants[j, k];
                                Determinants[j, k] = Determinants[j - 1, k];
                                Determinants[j - 1, k] = theTmpDec;
                            }
                        }
                        else
                        {
                            //将当前行减去上一行与theRate的积。
                            double theRate = Math.Round(Determinants[j, i] / Determinants[j - 1, i], ConstDef.Decimals);
                            for (int k = 0; k < theN; k++)
                            {
                                Determinants[j, k] = Math.Round(Determinants[j, k] - Determinants[j - 1, k] * theRate, ConstDef.Decimals);
                            }
                        }
                    }
                }
            }
            //结果为对角线上的元素的乘积，注意符号的处理。
            double theRetDec = theSign;
            for (int i = 0; i < theN; i++)
            {
                theRetDec *= Determinants[i, i];
            }
            return theRetDec;
        }

2.MyMathLib.LinearAlgebra.EquationsElimination

        /// <summary>
        /// 方程组消元，最后一列为系数,结果就在CoefficientDeterminant里.
        /// 本算法也可以用来求矩阵的秩.
        /// </summary>
        /// <param name="CoefficientDeterminant">方程组系数数组</param>
        public static void EquationsElimination(double[,] CoefficientDeterminant)
        {
            var theRowCount = CoefficientDeterminant.GetLength(0);
            var theColCount = CoefficientDeterminant.GetLength(1);
            int theN = theRowCount;
            int theE = theColCount - 1;
            //从第1列到第theE-1列,最后一列不用处理.
            for (int i = 0; i < theE; i++)
            {
                //从第theN-1行到第1行，将D[j,i]依次变为0,需要注意的是：
                //如果第j-1行，的左元素全部为0，才能继续交换.
                for (int j = theN - 1; j > 0; j--)
                {
                    //如果为当前值为0，则不处理,继续处理上一行
                    if (CoefficientDeterminant[j, i] == 0)
                    {
                        continue;
                    }
                    //******这里增加修改了判断是否继续交换消元的条件:
                    //如果左上邻元素[j-1, i-1]以及其左边的元素都为0方可交换
                    //因为当前元素的左边元素已经全部是零，因此如果要交换不能使本行左边产生非零数，
                    //则需要左上邻及其所有元素皆为0.
                    var theCanDo = true;
                    for (int s = i - 1; s >= 0; s--)
                    {
                        if (CoefficientDeterminant[j - 1, s] != 0)
                        {
                            theCanDo = false;
                            break;
                        }
                    }
                    if (theCanDo)
                    {
                        //如果[j,i]的上一行[j-1, i]的值为0则交换
                        if (CoefficientDeterminant[j - 1, i] == 0)
                        {
                            for (int k = 0; k <= theE; k++)//这里要交换常数项，所以是k <= theE
                            {
                                double theTmpDec = CoefficientDeterminant[j, k];
                                CoefficientDeterminant[j, k] = CoefficientDeterminant[j - 1, k];
                                CoefficientDeterminant[j - 1, k] = theTmpDec;
                            }
                        }
                        else
                        {
                            //将当前行减去上一行与theRate的积。
                            //var theRate = CoefficientDeterminant[j, i] / CoefficientDeterminant[j - 1, i];
                            //for (int k = 0; k <= theE; k++)//这里要计算常数项，所以是k <= theE
                            //{
                            //    CoefficientDeterminant[j, k] = CoefficientDeterminant[j, k] - CoefficientDeterminant[j - 1, k] * theRate;
                            //}
                            //改进：做乘法，可以避免小数换算带来的误差
                            var theRate2 = CoefficientDeterminant[j, i];
                            var theRate1 = CoefficientDeterminant[j - 1, i];
                            for (int k = 0; k <= theE; k++)//这里要计算常数项，所以是k <= theE
                            {
                                CoefficientDeterminant[j, k] = CoefficientDeterminant[j, k] * theRate1 - CoefficientDeterminant[j - 1, k] * theRate2;
                            }
                        }
                    }
                }
            }
        }

MyMathLib系列(订正两个函数)