Is b in the span of {w_1, .. , w_p}? Suppose b is in the span of { v_1 , ... , v_n }, and that each v_i is in the span of { w_1, ... , w_p }. Is b, then, in the span of { w_1, ... , w_p } ? If not, how could you modify the proposition so that it is true?
Not sure at all how to approach this.

$b\in \text{span}\{v_1,v_2,\cdots,v_n\}$
$v_i\in \text{span}\{w_1,w_2,\cdots,w_n\}$, i.e., $\{v_1,v_2,\cdots,v_n\}\subset \text{span}\{w_1,w_2,\cdots,w_n\}$ and hence $\text{span}\{v_1,v_2,\cdots,v_n\}\subset \text{span}\{w_1,w_2,\cdots,w_n\}$.
So $b\in \text{span}\{w_1,w_2,\cdots,w_n\}$.
Hi, Brian. You'd better read your textbooks carefully before doing homework. We learn mathematics by understanding definitions, theorems and properties instead of thinking all by ourselves. Good luck.
