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 value y[0] is specified to be zero. Does this change your answer to either part (a) or part (b)?
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