I was reading over some notes on vector bundles which make use of the following fact:
If $X$ is a $n$-manifold and $V$ is a real vector bundle on $X$ of rank $k$, then there exists a surjective map of vector bundles from the trivial bundle $X \times \mathbb{R}^{n+k} \to V$.
I'm not very accustomed to working with bundles. Can someone give an argument for this?