Let $X=\{x_1,...,x_n\}$ and $V$ a vector space of dimension $3$. What is the dimension of $\mathcal F(X,V)$ (set of function $X\to V$) and give a base of it.
I can imagine that it's $3n$ the dimension, but how can I get a base of it ? I tried to find linear independent function that generate the space, but I don't really see how it work.