Final answer:
The given LTI system with impulse response h(t) = (t + 1)u(t - 1) is not memoryless because its output depends on past inputs. However, it is causal because the output at any time t only depends on the present and past inputs and not future ones.
Step-by-step explanation:
To determine whether the given LTI (Linear Time-Invariant) system with impulse response h(t) = (t + 1)u(t - 1) is memoryless and/or causal, we must look at the properties of the system described by its impulse response.
A system is memoryless if the output of the system at any time t depends only on the input at that same time t. Since the impulse response of the system involves a time-shifted step function u(t - 1), it implies that the system output depends on past values (inputs before time t). Therefore, the system is not memoryless.
A system is causal if it is non-anticipative, meaning the output at any time depends only on present and past inputs and not on future inputs. Since u(t - 1) equals 0 for t < 1 and nonzero for t ≥ 1, the system does not respond before the input is applied. This indicates that the system is causal because the output only depends on current and past inputs.