Is \(\mathbb{Q}^3\) a subspace of \(\mathbb{C}^3\) if the set of
scalars is \(\mathbb{Q}\)?
The answer is “Yes”.
Since the set of complex numbers contains the set of rational numbers,
\(\mathbb{Q}^3\) is a subset of \(\mathbb{C}^3\).
Also, \(\mathbb{Q}^3\) and \(\mathbb{C}^3\) are both
a vector spaces over \(\mathbb{Q}\).