For the following system of linear equations determine the values of k for which it has (i) no solutions, (ii) infinitely many solutions, and (iii) a unique solution. For those values of k where solutions exist, find what those solutions are.
I am trying to do this with Gaussian or Gauss-Jordan elimination
2x1 + 6x2 - 4x3 = 0
3x1 + 9x2 - 6x3 = 0
-4x1 - 12x2 + kx3 = 0
I'm familiar with how to do Gaussian elimination, but I don't know how to go about solving each of the situations they ask for.