4×4 Matrices

4×4 Matrices

Matrices are the engine of 3D transformations. A 4×4 matrix transforms a tuple (a point or vector) by multiplying them together.

Storing a Matrix

We'll store a 4×4 matrix as 16 values in a flat array (row-major order):

class Matrix4 {
public:
    Matrix4(double a, double b, double c, double d,
            double e, double f, double g, double h,
            double i, double j, double k, double l,
            double m, double n, double o, double p) {
        this->data = [a,b,c,d, e,f,g,h, i,j,k,l, m,n,o,p];
    }
    double get(int row, int col) const {
        return this->data[row * 4 + col];
    }
};

get(row, col) retrieves element at row row and column col.

Matrix Multiplication

Multiplying two 4×4 matrices: element [row][col] of the result is the dot product of row row from A with column col from B:

double matElement(Matrix4 A, Matrix4 B, int row, int col) {
    double sum = 0;
    for (int k = 0; k < 4; k++) {
        sum += A.get(row, k) * B.get(k, col);
    }
    return sum;
}

Your Task

Implement matElement(Matrix4 A, Matrix4 B, int row, int col) that computes a single element of the matrix product A × B.

From the book's test case:

A = [1,2,3,4; 5,6,7,8; 9,8,7,6; 5,4,3,2]
B = [-2,1,2,3; 3,2,1,-1; 4,3,6,5; 1,2,7,8]
A*B[0][0] = 20, A*B[1][2] = 114

Expected output:

20
114