TIFR ECE 2021 | Question: 1

Question

Consider a system with input $x(t)$ and output $y(t)$ such that
\[y(t)=t \;x(t) .\]

Consider the following statements:

1. The system is linear.
2. The system is time-invariant.
3. The system is causal.

Then which of the following is $\text{TRUE?}$

• A. Only statement $1$ is correct.
• B. Only statement $2$ is correct.
• C. Only statement $3$ is correct.
• D. Only statements $1$ and $3$ are correct.
• E. All three statements $1, 2,$ and $3$ are correct.