Condition of a system of equations to have infinitly many solutions

[fluidistic]

0. Homework Statement
For which values of "a" the following system of equations has a unique solution? Infinitly many solutions?
x-y+z=2
ax-y+z=2
2x-2y+(2-a)z=4a

1. The attempt at a solution

I've put the system of equations under an amplied matrix and I reduced it.
I finally got the 3x3 identity matrix with the corresponding vector solution : { (4-8a+a²)/(1-a) ; (3a-2)/(2a-1)*(-2+6a-4a²)/(1-a)² ; (-2+6a-4a²)/(1-a)² ) }
I don't know what to do from here.
I see that "a" cannot be equal to 1 in the vector solution, but it could be equal to 1 in the original system of equations. So I probably did at least one error. But still, say the result is what I got, what do I have to do to find out the values of "a" satisfying the conditions of the question?

 

[chrisk]

Try using Cramer's Rule. If the denominater determinate equals zero then the solutions are inconsistent or dependent. For an infinite number of solutions, the numerator determinate will equal zero for each variable.