使用克莱姆法则求解线性方程组时结果异常的问题排查

你的代码结果不符合预期，核心问题是完全偏离了克莱姆法则的计算逻辑，同时存在语法和拼写错误，以下是具体问题和修正方案：

错误点分析 #

1. 无意义的中间变量
   你定义的c1 = a1 + b1和c2 = a3 + b2没有任何数学依据，克莱姆法则不需要这类变量，属于错误设定。

2. 行列式计算完全错误
   针对你的方程组：

   3x - 4y = 15
   -6x + y = -9
   

   按照克莱姆法则，正确的行列式计算应该是：

   • 系数行列式 D = (3*1) - (-4*-6) = 3 - 24 = -21
   • x替换行列式 Dx = (15*1) - (-4*-9) = 15 - 36 = -21
   • y替换行列式 Dy = (3*-9) - (15*-6) = -27 + 90 = 63
     而你的代码中D、Dx、Dy的计算逻辑完全错误，这是导致结果偏差的根本原因。

3. 条件判断语法与拼写错误

   • 条件If D And Dy And Dx = 0 Then语法错误，VB中需要逐一判断每个变量是否为0，正确写法是If D = 0 And Dy = 0 And Dx = 0 Then
   • 存在多处拼写错误：Infinte→Infinite，inconsistant→inconsistent，indepent→independent

修正后的代码 #

Dim a1 As Double, a2 As Double, b1 As Double, a3 As Double, a4 As Double, b2 As Double
Dim D As Double, Dx As Double, Dy As Double, X As Double, Y As Double

Console.WriteLine("Input the coefficients of the first equation: a11, a12, b1: ")
Console.WriteLine()
Console.WriteLine("a1 = ")
a1 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine("a2 = ")
a2 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine("b1 = ")
b1 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine()
Console.WriteLine("Input the coefficients of the second equation: a21, a22, b2: ")
Console.WriteLine()
Console.WriteLine("a3 = ")
a3 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine("a4 = ")
a4 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine("b2 = ")
b2 = Convert.ToDouble(Console.ReadLine())
Console.WriteLine()
Console.WriteLine("Output the system of equations: ")
Console.WriteLine()
Console.WriteLine("({0})x + ({1})y = {2}", a1, a2, b1)
Console.WriteLine()
Console.WriteLine("({0})x + ({1})y = {2}", a3, a4, b2)
Console.WriteLine()

' 克莱姆法则正确计算行列式
D = a1 * a4 - a2 * a3
Dx = b1 * a4 - a2 * b2
Dy = a1 * b2 - b1 * a3

' 处理解的不同情况
If D = 0 Then
    If Dx = 0 And Dy = 0 Then
        Console.WriteLine("Infinite Solutions! The system is consistent and dependent.")
    Else
        Console.WriteLine("No solutions! The system is inconsistent.")
    End If
Else
    X = Dx / D
    Y = Dy / D
    Console.WriteLine("A unique solution! The system is consistent and independent.")
    Console.WriteLine()
    Console.WriteLine("x = {0}", X)
    Console.WriteLine("y = {0}", Y)
End If

Console.ReadLine()

验证说明 #

输入你提供的方程组系数：

• 第一个方程：a1=3，a2=-4，b1=15
• 第二个方程：a3=-6，a4=1，b2=-9

运行修正后的代码，会得到正确结果：x=1，y=-3。

内容的提问来源于stack exchange，提问作者David