Suppose v1,…,vm∈V. Let
A={λ1v1+⋯+λmvm:λ1,…,λm∈F and λ1+⋯+λm=1}.
- Prove that A is an affine subset of V
- Prove that every affine subset of V that contains v1,…,vm also contains A.
- Prove that A=v+U for some v∈V and subspace U of V with dimU≤m−1.
TODO