Vector space/General distributivity law/Exercise

Let ${}V$ be a vector space over a field ${}K$. Let ${}s_{1},\ldots ,s_{k}\in K$ and ${}v_{1},\ldots ,v_{n}\in V$. Show

${}{\left(\sum _{i=1}^{k}s_{i}\right)}\cdot {\left(\sum _{j=1}^{n}v_{j}\right)}=\sum _{1\leq i\leq k,\,1\leq j\leq n}s_{i}\cdot v_{j}\,.$

Create a solution