Can someone please show me how to prove $||Ax||_2 \leq ||A||_2 ||x||_2$, where $||A||_2$ is the spectral norm and $ A \in \mathbb{R^{n \times n}} $ and $x \in \mathbb{R^n}$.
So far I tried to write the statement out in coordinates and then simplify, but now I'm stuck (I don't know what to do with the max eigenvalue).