Final answer:
The impulse response h₁(t) corresponds to an unstable system due to the exponential growth for t → -∞. In contrast, h₂(t) corresponds to a stable LTI system because it is absolutely integrable, indicating that it will produce bounded outputs for all bounded inputs.
Step-by-step explanation:
When determining whether the given impulse responses correspond to stable LTI systems, we must check if the outputs of the systems remain bounded for all bounded inputs. This typically involves checking whether the impulse responses themselves are absolutely integrable over their entire domain, or equivalently, if the area under their magnitude curves is finite.
For the impulse response h₁(t) = e(1−j)t u(−t), this function is not absolutely integrable because the exponential term e⁴t grows without bound as t → -∞. Therefore, the system associated with h₁(t) is unstable.
In contrast, for h₂(t) = e−t sin(−t) u(t), the factor e−t ensures that the response decays exponentially for positive t, while sin(−t) introduces oscillation that does not affect stability. Since this impulse response is absolutely integrable over its domain t ≥ 0, the system corresponding to h₂(t) is stable.