The system represented by equations

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The system represented by equations—
(i) y[n] = anx(n) + b
(ii) y[n] = e^x[n]

1. (i) is linear, (ii) is non-linear
2. (i) is non-linear, (iii) is linear
3. both (i) and (ii) are linear
4. both (i) and (ii) are non-linear

Correct Option: D

(i) y(n) = anx(n) + b
F[x₁(n) + x₂(n)] = an[x₁(n) + x₂(n)] + b F[x₁(n)] + F[x₂(n)]
= [an x₁(n) + b] + [an x₂(n) + b]
= an[x₁(n) + x₂(n)] + 2b
Therefore,
F[x₁(n) + x₂(n)] ≠ F[x₁(n)] + F[x₂(n)]
Hence, the system is non-linear.
(ii) y(n) = e^x(n)
F[x₁(n) + x₂(n)] = e^{[x₁ (n) + x₂ (n)]}
= e^x₁(n) + e^x₂(n)
F[x₁(n)] + F[x₂(n)] = e^x₁(n) + e^x₂(n)
Since here,
F[x₁(n) + x₂(n)] ≠ F[x₁(n)] + F[x₂(n)]
Hence, the system is non-linear, therefore alternative (D) is the correct choice.