Question: Consider a system with input x[n] and output y[n] that satisfy the difference equation y[n] = ny[n 1] + x[n]. The system is causal

Consider a system with input x[n] and output y[n] that satisfy the difference equation 

y[n] = ny[n – 1] + x[n].

The system is causal and satisfies initial-rest conditions; i.e., if x[n] = 0 for n <  n0, then y[n] = 0 for n < n0.

(a) If x[n] = δ[n], determine y[n] for all n.

(b) Is the system linear? Justify your answer.

(c) Is the system time invariant? Justify your answer.

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