我在二维数组中给出了错误的结果

Question

你好，我正在制作一个 c-sharp windows 形式的行列式计算器，但我对求和结果有疑问。该算法是：总和 = (row11((row22 * row33) - (row23 * row32))) - (row12 ((row21 * row33) - (row23 - row31))) + (row13((row21 * row32) - (row22 - row31) ));

例如这是一个矩阵：|1,2,3| |2,3,4| |5,6,7| 结果应该是 0 但在我的代码中我给出 25

public void cal()
    {
        int[,] a = new int[3, 3];

        int row11;
        int row12;
        int row13;

        int row21;
        int row22;
        int row23;

        int row31;
        int row32;
        int row33;

        row11 = Convert.ToInt32(textBox1.Text);
        row12 = Convert.ToInt32(textBox2.Text);
        row13 = Convert.ToInt32(textBox3.Text);

        row21 = Convert.ToInt32(textBox4.Text);
        row22 = Convert.ToInt32(textBox5.Text);
        row23 = Convert.ToInt32(textBox6.Text);

        row31 = Convert.ToInt32(textBox7.Text);
        row32 = Convert.ToInt32(textBox8.Text);
        row33 = Convert.ToInt32(textBox9.Text);


        a[0, 0] = row11;
        a[0, 1] = row12;
        a[0, 2] = row13;

        a[1, 0] = row21;
        a[1, 1] = row22;
        a[1, 2] = row23;

        a[2, 0] = row31;
        a[2, 1] = row32;
        a[2, 2] = row33;

        int sum = (row11 * ((row22 * row33) - (row23 * row32))) - (row12 * ((row21 * row33) - (row23 - row31))) + (row13 * ((row21 * row32) - (row22 - row31)));

        textBox19.Text = sum.ToString();

Answer 1

通过分解行列式计算我得到了你的样本 0:

        var determinant = a[0, 0] * (a[1, 1] * a[2, 2] - a[2, 1] * a[1, 2]) -
                          a[0, 1] * (a[1, 0] * a[2, 2] - a[2, 0] * a[1, 2]) +
                          a[0, 2] * (a[1, 0] * a[2, 1] - a[2, 0] * a[1, 1]);

我在二维数组中给出了错误的结果

i give wrong result in 2d arrays

c#

arrays

2d

matrix

calculation