Determine all values of k for which the given system has an infinite number of solutions:

1x1 + 2x2 + x3 = kx1

2x1 + 1x2 + 1x3 = kx2

1x1 +1 x2 + 2x3 = kx3

I know it is probably as simple as finding the determinant and then applying the properties of the determinant, but I am thrown off by the fact that k is in the solutions column. Please help! Thanks in advance.