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Consider a continuous-time system with input x(t) and output y(t) given by y(t) = x(t) cos(t). This system is

1. linear and time-invariant
2. non-linear and time-invariant
3. linear and time-varying
4. non-linear and time-varying

Correct answer: linear and time-varying

Solution

The system is linear because it satisfies the principles of superposition, meaning that the output for a sum of inputs is the sum of the outputs for each input. However, it is time-varying because the output depends on the time-varying function cos(t), which alters the system's behavior over time.

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