Question

Determine whether the following system is linear, time invariant or both: y(t) = t²x (t – 1)

a.linear, but not time invariant
b.time invariant, but not linear
c.neitherilinear nor time invariant
d.both linear and time invariant

Answer 1

The given system is neither linear nor time invariant.

Step-by-step explanation:

The given system is neither linear nor time invariant, so the correct answer is option c.

A system is considered linear if it satisfies the principle of superposition, which means that if input A produces output X and input B produces output Y, then any combination of A and B should produce a corresponding combination of X and Y.

A system is considered time invariant if its behavior does not change over time. In other words, if a particular input produces a certain output at time t, then the same input should produce the same output at any other time.

The given system, y(t) = t²x(t – 1), does not satisfy these conditions and is therefore neither linear nor time invariant.