Gauss elimination

public static double[] SolveSystem(double[][] typeMatrix, double[] grades)
{
    const double eps = 1e-9;
    double[][] matrix = typeMatrix.Select(x => x.ToArray()).ToArray();
    double[] column = grades.ToArray();
    int m = matrix.Length, n = matrix[0].Length;
    var resRows = Enumerable.Repeat(-1, n).ToArray();

    for (int col = 0, row = 0; row < m && col < n; col++)
    {
        double max = Enumerable.Range(row, m - row).Max(r => Math.Abs(matrix[r][col]));
        int xrow = Enumerable.Range(row, m - row).First(r => Math.Abs(matrix[r][col]) == max);
        if (Math.Abs(matrix[xrow][col]) < eps)
            continue;
        Swap(ref matrix[row], ref matrix[xrow]);
        Swap(ref column[row], ref column[xrow]);
        for (int r = 0; r < m; r++)
            if (r != row && Math.Abs(matrix[r][col]) >= eps)
            {
                double coef = matrix[r][col] / matrix[row][col];
                for (int c = col; c < n; c++)
                    matrix[r][c] -= matrix[row][c] * coef;
                column[r] -= column[row] * coef;
            }
        resRows[col] = row++;
    }
    return resRows.Select((row, col) => row < 0 ? 0 : column[row] / matrix[row][col]).ToArray();
}