因为向量和矩阵的计算工作量比较大，为了更好的书写代码，这里增加了几个定义类，这些定义或者扩展方法将在以后的代码中应用到：
1、公共枚举类型

/*
   文件:PublicEnums.cs
 * 目的：定义公共枚举类型.
 */
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace MyMathLib
{
    /// <summary>
    /// 初等变换类型(课本上是加，这里是减，仅仅是个系数符号的区别.
    /// </summary>
    public enum BasicTransMethod
    {
        /// <summary>
        /// 交换i< == >j
        /// </summary>
        Swap,
        /// <summary>
        /// 乘以非零数:i=i*M
        /// </summary>
        Multipler,
        /// <summary>
        /// 第i行减去第j行乘以一个系数:i=i-j*M
        /// </summary>
        CoPlus1,
        /// <summary>
        /// 第i行乘以系数减去第j行乘以一个系数:i=i*M1 - j*M2
        /// </summary>
        CoPlus2

    }
    /// <summary>
    /// 行变换还是列变换.
    /// </summary>
    public enum TransRowOrCol
    {
        /// <summary>
        /// 行
        /// </summary>
        Row,
        /// <summary>
        /// 列
        /// </summary>
        Col
    }

    public static class ConstDef
    {
        public const int Decimals = 15;
    }

    public enum SolutionType
    {
        /// <summary>
        /// 无解
        /// </summary>
        None,
        /// <summary>
        /// 只有零解
        /// </summary>
        OnlyZero,
        //仅有一个非零解
        OnlyOne,
        /// <summary>
        /// 有很多解.
        /// </summary>
        Many
    }
}

2、方程求解结果

/*
 * SolutionOfEquation.cs
 * Added by Hawksoft.
 */
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace MyMathLib
{
    /// <summary>
    /// 方程解结果,用于方程组求解后的结果存放.
    /// </summary>
    public class SolutionOfEquation
    {
        /// <summary>
        /// 解类型
        /// </summary>
        public SolutionType SolutionType{ get; set; }
        /// <summary>
        /// 解向量
        /// </summary>
        public List<double[]> SolutionVectors { get; set; }
        /// <summary>
        /// 基本未知量
        /// </summary>
        public List<int> PrimaryUnknownVariations { get; set; }
        /// <summary>
        /// 自由未知量.
        /// </summary>
        public List<int> FreeUnknownVariations { get; set; }

        public SolutionOfEquation()
        {
            SolutionVectors = new List<double[]>();
            PrimaryUnknownVariations = new List<int>();
            FreeUnknownVariations = new List<int>();
        }
    }
}

3、初等变换记录项

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace MyMathLib
{
    /// <summary>
    /// 初等变换记录项,用于矩阵初等变换的过程演示和矩阵求逆.
    /// </summary>
    public class TransformItem
    {
        public BasicTransMethod TransMethod { get; set; }
        public int i { get; set; }
        public int j { get; set; }
        public double M1 { get; set; }
        public double M2 { get; set; }
        public TransRowOrCol RowOrCol { get; set; }

        public static TransformItem CreateEleTransRow1(int i, int j)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = 1,
                TransMethod = BasicTransMethod.Swap,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransRow2(int i,double Multipler)
        {
            return new TransformItem()
            {
                i = i,
                j = i,
                M1 = Multipler,
                M2 = Multipler,
                TransMethod = BasicTransMethod.Multipler,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransRow3(int i, int j,double Multipler)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = Multipler,
                M2 = Multipler,
                TransMethod = BasicTransMethod.CoPlus1,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransRow4(int i, int j, double M1,double M2)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = M1,
                M2 = M2,
                TransMethod = BasicTransMethod.CoPlus2,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransCol1(int i, int j)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = 1,
                M2 = 1,
                TransMethod = BasicTransMethod.Swap,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransCol2(int i, double Multipler)
        {
            return new TransformItem()
            {
                i = i,
                j = i,
                M1 = Multipler,
                M2 = Multipler,
                TransMethod = BasicTransMethod.Multipler,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransCol3(int i, int j, double Multipler)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = 1,
                M2 = Multipler,
                TransMethod = BasicTransMethod.CoPlus1,
                RowOrCol = TransRowOrCol.Row
            };
        }
        public static TransformItem CreateEleTransCol4(int i, int j, double M1,double M2)
        {
            return new TransformItem()
            {
                i = i,
                j = j,
                M1 = M1,
                M2 = M2,
                TransMethod = BasicTransMethod.CoPlus2,
                RowOrCol = TransRowOrCol.Row
            };
        }
    }

另外说明一下：原来一直用decimal来计算，但在矩阵计算测试中发现，decimal很容易爆仓，所以改用double类型，其实decimal的位数比double多很多，但由于其特殊性，其表达的范围要比double小，所以后面改成了double.

MyMathLib系列(向量及矩阵--准备工作)