1) Show that:
The following inequalities hold for
all $x \in \mathbb{R}^n$ (or $x \in \mathbb{C}^n$):
$\|x\|_\infty \le \|x\|_1 \le n \|x\|_\infty$,
$\|x\|_\infty \le \|x\|_2 \le \sqrt{n} \|x\|_\infty$,
$\|x\|_2 \le \|x\|_1 \le \sqrt{n} \|x\|_2$.
If you can show any one of them that is enough, as the others are equivalent.