A single input-output relationship is given for each of the following three systems:

(a) System A: x[n] = (1/3)ⁿ,      y[n] = 2(1/3)ⁿ.

(b) System B: x[n] = (1/2)ⁿ,      y[n] = (1/4)ⁿ.

(c) System C: x[n] = (2/3)ⁿu[n],           y[n] = 4(2/3)ⁿu[n] – 3(1/2)ⁿu[n].

Based on this information, pick the strongest possible conclusion that you can make about each system from the following list of statements:

(i) The system cannot possibly be LTI.

(ii) The system must be LTI.

(iii) The system can be LTI, and there is only one LTI system that satisfies this input-output constraint.

(iv) The system can be LTI, but cannot be uniquely determined from the information in this input-output constraint.

If you chose option (iii) from this list, specify either the impulse response h[n] or the frequency response H(e^jω) for the LTI system.