Q1: Let $M \subseteq \mathbb{R}^n$. Is $\mathrm{Span}(M)$ a linear subspace?

A1: Yes!

A2: No!

A3: Only in special cases.

Q2: What is $\mathrm{Span}(\emptyset)$?

A1: ${ \mathbf{0} }$

A2: $ \mathbb{R}^n $

A3: ${ \mathbf{v} \in \mathbb{R}^n \mid \mathbf{v} \neq \mathbf{0} }$

Q3: Let $U,V \subseteq \mathbb{R}^n$ be two subspaces. Which claim is not correct?

A1: $U \subseteq \mathrm{Span}(U \cup V)$

A2: $V \subseteq\mathrm{Span}(U \cup V)$

A3: $U \cap V \subseteq\mathrm{Span}(U \cup V)$

A4: $\mathrm{Span}(U \cup V)$ is a subspace.

A5: ${0 } \cap \mathrm{Span}(U \cup V) = \emptyset$