Is the following system linear?

Question

This might be trivial, but can't seem to get an intuitive understanding of proving the linearity of a system defined as such:

$y(t) = 0$, $y(t)$ is the response of system from input $x(t)$

The system is linear when the following two properties hold:

$a \cdot x(t)$ corresponds to a system response of $a \cdot y(t)$ where $a$ is a scalar

$x_1(t) + x_2(t)$ corresponds to a system response of $y_1(t) + y_2(t)$

I can't seem to make the connection to the linearity conditions above because the system response is defined not in terms of $x(t)$.

Answer 1

If by $y(t) = 0$ you mean the response of this system to every input is $0$ (not just a particular $x(t)$), then yes, this is linear. $a \cdot 0 = 0$, and $0 + 0 = 0$.