This may seem obvious, but how would you explain something like this? This is referring to the homogeneous system of differential equations, originally from
$$x'(t) = A(t)x(t) + b(t)$$
where $b(t) = 0$ to bring us the homogeneous system.
I ask about $x=0$ being a solution because it is necessary to demonstrate that the set of all solutions $x$ is a subspace of $V_n(I)$.