Which of the following properties is NOT an axiom of a vector space?
Question 2
Consider the set of all $2 \times 2$ matrices with real entries, denoted as $\text{M}_{2 \times 2}(\mathbb{R})$. If we define vector addition as standard matrix addition and scalar multiplication as standard scalar multiplication of matrices, what is the zero vector in this space?
Question 3
Given a vector space $V$ and a subset $W \subseteq V$. Which of the following conditions is NOT required for $W$ to be a subspace of $V$?
Question 4
Which of the following sets of vectors is linearly dependent in $\mathbb{R}^3$?
Question 5
If a set of vectors $B = \{\mathbf{v}_1, \mathbf{v}_2, \ldots, \mathbf{v}_n\}$ forms a basis for a vector space $V$, what does this imply about the vectors in $B$?
