Determine the values of the constant k that result in an infinite number of solutions for the given system. Use the determinant approach. Which of the following systems of equations represents the given system?

A) x + 2y + kz = 0
2x - ky + z = 0
3x + 6y + z = 0

B) x + 2y + kz = 0
2x - ky + z = 0
3x + 6y + z = 0

C) x + 2y + kz = 0
2x - ky + z = 0
3x + 6y + z = 0

D) x + 2y + kz = 0
2x - ky + z = 0
3x + 6y + z = 0