Affine space/Finite point family/Affine basis/Characterization/Exercise

Let ${}E$ be an affine space over the ${}K$-vector space ${}V$, and let ${}P_{1},\ldots ,P_{n}$ be a finite family of points in ${}E$. Show that the following statements are equivalent.

1. The points form an affine basis of ${}E$.
2. The points form a minimal affine generating system of ${}E$.
3. The points are maximally affinely independent.

Create a solution