Final answer:
The question pertains to verifying the equality of sequences resulting from different input methods in a potentially linear system. The comparison and principles of wave superposition are used to determine system linearity in physics.
Step-by-step explanation:
The question involves analyzing the linearity of a system based on the comparison of output sequences obtained by different methods of input combination. Specifically, it asks whether the sequence y[n] (obtained with weighted input) is equal to yt[n] (obtained by combining outputs y1[n] and y2[n] with the same weights). If both sequences are equal, this infers that the system behaves linearly, adhering to the principle of superposition. In the context of wave functions, the principle of superposition dictates that the sum of two waves is also a solution to the wave equation, which indicates linearity. An example provided is the superposition of two waves that differ by a phase shift, resulting in a combined wave that satisfies theoretical expectations.
The sequence comparison and the discussion around superposition and linearity are essential to determine the characteristic of the system. Examples related to wave functions demonstrate the property of superposition. In the context of linear systems, the principle is fundamental in understanding how inputs are related to outputs.(b) The system is linear if the superposition principle holds, meaning that if you combine two inputs y1[n] and y2[n] with different weights, the resulting output should be equal to the weighted sum of the individual outputs. You can justify whether the system is linear by checking if it satisfies the superposition principle for a range of inputs.