Finding the determinant of a matrix

Question

I'm working on a program where I have to write a method that will find the determinant of a matrix and I'm having some trouble. This is what I have so far.

public Matrix determinant() {
Matrix determinantM = new Matrix(this.rows, this.columns);
for(int r = 0; r < 3; r++) {
    for (int c = 0; c < 3; c++) {
        determinantM.data[r][c] = this.data[r][c];
    }
}
Matrix x = (determinantM.data[1][1] * determinantM.data[2][2]) - (determinantM.data[2][1] * determinantM.data[1][2]);
Matrix y = (determinantM.data[1][0] * determinantM.data[2][2]) - (determinantM.data[2][0] * determinantM.data[1][2]);
Matrix z = (determinantM.data[1][0] * determinantM.data[2][1]) - (determinantM.data[2][0] * determinantM.data[1][1]);

Matrix newD = (determinantM.data[0][0] * x) - (determinantM.data[0][1] * y) + (determinantM.data[0][2] * 2);
return newD;
}

and this is how I'm trying to call it from main

 Matrix z = new Matrix(new double[][]{{1, 2, 3},{0, 4, 5},{1, 0, 6}});
    Matrix v = z.determinant();
    System.out.println("v:\n" + v);

I'm not really sure if this is the right way to approach this problem or if I just have some mistakes within my code. I would really appreciate any help.

Answer 1

As stated here to calculate the determinant of a 3x3 matrix like:

a b c
d e f
g h i

The determinant will be:

|A| = a(ei − fh) − b(di − fg) + c(dh − eg)

Therefore, this part of your code:

    Matrix x = (determinantM.data[1][1] * determinantM.data[2][2]) - (determinantM.data[2][1] * determinantM.data[1][2]);
    Matrix y = (determinantM.data[1][0] * determinantM.data[2][2]) - (determinantM.data[2][0] * determinantM.data[1][2]);
    Matrix z = (determinantM.data[1][0] * determinantM.data[2][1]) - (determinantM.data[2][0] * determinantM.data[1][1]);

should actually be:

double x=(determinantM.data[0][0] * (determinantM.data[1][1] * determinantM.data[2][2] – determinantM.data[1][2] * determinantM.data[2][1]));
double y=(determinantM.data[0][1] * (determinantM.data[1][0] * determinantM.data[2][2] – determinantM.data[1][2] * determinantM.data[2][0]));
double z=(determinantM.data[0][2] * (determinantM.data[1][0] * determinantM.data[2][1] – determinantM.data[1][1] * determinantM.data[2][0]));

Then the determinate would be x - y + z;

So you final method should be something like:

public double determinant() {
     double x=(determinantM.data[0][0] * (determinantM.data[1][1] * determinantM.data[2][2] – determinantM.data[1][2] * determinantM.data[2][1]));
     double y=(determinantM.data[0][1] * (determinantM.data[1][0] * determinantM.data[2][2] – determinantM.data[1][2] * determinantM.data[2][0]));
     double z=(determinantM.data[0][2] * (determinantM.data[1][0] * determinantM.data[2][1] – determinantM.data[1][1] * determinantM.data[2][0]));

     return x - y + z;
 }

Since you are not modifying the original matrix, you do not need to make a copy out of it.

This code naturally, only works for matrix 3x3.