System of linear equations in C Find all solutions for matrix depending on the parametres a,b ∈ C...

With the usage of elementary row operations we can get to the reduced matrix
Now, what is the appropriate way of the parametrical solution and how do parametres a,b affect our solutions (existece, values, # of solutions...)?
thought it was obvious from the first matrix.. the columns represent variables x1, x2, x3 plus we have the parameters a, b.
The system would look like this:


-ix1 + ax2 + (2-4i)x3 = 0
x1 + 2ix2 + bx3 = 0
ix1 - x2 + ix3 = 1
thought it was obvious from the first matrix.. the columns represent variables x1, x2, x3 plus we have the parameters a, b.
The system would look like this:


-ix1 + ax2 + (2-4i)x3 = 0
x1 + 2ix2 + bx3 = 0
ix1 - x2 + ix3 = 1