題組內容

8 Let $\| \cdot \| : M_{2 \times 2}(\mathbb{R}) \to \mathbb{R}$ be a function defined by $\| A \| = \max_{x \in S} \| Ax \|_2$, where $S = \{x \in \mathbb{R}^2 | \| x \|_2 = 1\}$.

b. (10) Show that $(M_{2 \times 2}(\mathbb{R}), \| \cdot \|)$ is a normed space.