= Solution
{c}
Every $v\in V$ has a unique <basis> expansion $v=\sum_{i=1}^n a_iv_i$. Define the <linear functional>
$$
\boxed{T\left(\sum_{i=1}^n a_iv_i\right)=\sum_{i=1}^n a_i\mu_i.}
$$
Uniqueness of the <coordinates> makes this definition well defined. The <coordinates> of a sum or a <scalar multiple> are the corresponding sums or <scalar multiples> of the <coordinates>, so this formula defines a <linear map>. It has $T(v_i)=\mu_i$. Conversely, any <linear map> with those values must satisfy the same formula by <linearity>, proving uniqueness.
If the <finite field> $\mathbb F$ has $q$ elements, each of the $n$ values $\mu_i$ can be chosen independently in $q$ ways. The number of <linear maps> $V\to\mathbb F$ is therefore $\boxed{q^n}$, including the zero <linear map>.
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