14. (V 1) (core) Prove that $H$ is a vector space by demonstrating that it satisfies the definition of a vector space or provide an example of a vector in Span $H$ that is not in $H$. $H = \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix} : a, b, c, d \in \mathbb{R} \right\}$ and $V$ is the vector space of all $2 \times 2$ matrices.