I'm given a set of vectors and asked if they are a basis for some vector space, say $V$. All the examples I've been given in class and found online simply prove linear independence. I'd even be willing to bet that my professor has stated that's good enough anyway.
But the few examples I've found for "working out" the spanning are confusing and just seem to be way over my head, or overly simplified (like $0x=0$); I understand the concept, but as long as the given subset has the same dimension as $V$ and is linearly independent, it will span... right? If so, what's the reason to actually bother with the span?