Given three vectors $\boldsymbol u,\,\boldsymbol v,\,\boldsymbol w$ in $\mathbb R^n$ that Span $\mathbb R^n$ then prove that the vectors $\boldsymbol u-2 \boldsymbol w,\, \boldsymbol v+\boldsymbol w$, and $\boldsymbol w$ span $\mathbb R^n$ as well. Hint: It helps to represent the original vectors $\boldsymbol u,\,\boldsymbol v,\,\boldsymbol w$ as linear combinations of these new vectors
Okay so I'm thinking this has to do with 'closure under addition'? I'm very confused by how to approach/solve this. Isn't w the same in both so obviously spans $\mathbb R^n$. All help is welcome and appreciated.