Linear mapping/Linear combinations/Exercise

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ and ${\displaystyle {}W}$ be ${\displaystyle {}K}$-vector spaces. Let

${\displaystyle \varphi \colon V\longrightarrow W}$

be a linear map. Prove that for all vectors ${\displaystyle {}v_{1},\ldots ,v_{n}\in V}$ and coefficients ${\displaystyle {}s_{1},\ldots ,s_{n}\in K}$, the relationship

${\displaystyle {}\varphi {\left(\sum _{i=1}^{n}s_{i}v_{i}\right)}=\sum _{i=1}^{n}\lambda _{i}\varphi (v_{i})\,}$

holds.