Solution 3e 11

Suppose $v_1,\dots,v_m \in V$ . Let

A = \{\lambda_1 v_1 + \dots + \lambda_m v_m : \lambda_1,\dots,\lambda_m \in \mathbf{F} \text{ and } \lambda_1 + \dots + \lambda_m = 1\}.

Prove that $A$ is an affine subset of $V$
Prove that every affine subset of $V$ that contains $v_1,\dots,v_m$ also contains $A$ .
Prove that $A = v + U$ for some $v \in V$ and subspace $U$ of $V$ with $\dim U \le m - 1$ .

TODO