A linear system: 

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  1. satisfies the properties of superposition and homogeneity
  2. satisfies the properties of superposition but not of homogeneity
  3. satisfies the properties of homogeneity but not of superposition
  4. does not satisfy the properties of superposition and homogeneity

Answer (Detailed Solution Below)

Option 1 : satisfies the properties of superposition and homogeneity
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Concept:

A linear system is one that satisfies two key mathematical properties:

  • Homogeneity (or scaling): If input x produces output y, then input αx produces output αy.
  • Superposition (or additivity): If input x₁y₁ and x₂y₂, then input x₁ + x₂y₁ + y₂.

Both these properties must be satisfied for a system to be classified as linear.

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