(Solution) - Consider a system with input x n and output y n The -(2025 Original AI-Free Solution)

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Consider a system with input x[n] and output y[n]. The input-output relation for the system is defined by the following two properties:
1. y[n] ? ay[n ? 1] = x[n],
2. y[0] = 1.
(a) Determine whether the system is time invariant.
(b) Determine whether the system is linear.
(c) Assume that the difference equation (property 1) remains the same, but the vale y[0] is specified to be zero. Does this change your answer to either Part (a) or part (b)?