Barycentric coordinates/Point representation/Exercise

Let ${}P$ be a point in an affine space ${}E$ over ${}V$. Show that the following expressions are barycentric combinations for ${}P$ (let ${}Q\in E$ and ${}v\in V$).

1. ${}P$.
2. ${}P+Q-Q$.
3. ${}(P+v)-(Q+v)+Q$.

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