[amp_mcq option1=”Linear and time-invariant” option2=”Linear and time varying” option3=”Non-linear & time-invariant” option4=”Non-linear and time-varying” correct=”option1″]
The correct answer is: A. Linear and time-invariant.
A linear system is a system that satisfies the following properties:
- Linearity: The output of a linear system is the sum of the outputs of the system due to each of the inputs, with the outputs scaled by the corresponding input values.
- Time-invariance: The output of a time-invariant system is the same for all inputs that are delayed by the same amount.
In this case, the system is described by the relation $y(t) = tx(t)$. This relation satisfies the linearity property because the output is the product of the input and a constant. It also satisfies the time-invariance property because the output is the same for all inputs that are delayed by the same amount. Therefore, the system is linear and time-invariant.
The other options are incorrect because they do not describe the system correctly. Option B is incorrect because the system is not time-varying. Option C is incorrect because the system is linear. Option D is incorrect because the system is time-invariant.