(a) Show that if a system is either additive or homogeneous, it has the property that if the input is identically zero, then the output is also identically zero.
(b) Determine a system (either in continuous or discrete time) that is neither additive nor homogeneous but which has a zero output if the input is identically zero.
(c) From part (a), can you conclude that if the input to a linear system is zero, between times t1 and t2 in continuous time or between times n1 and n2 in discrete time, then its output must also be zero between these same times? Explain your answer.
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