For #1, recall that the condition for a set
to span some space V (over a field F), is that
, there exist some scalars
, not all zero, such that
. That is to say, any element in V can be expressed as a linear combination of the set's elements.
In this question we are given that this is correct for the set
and we need to prove that it is also correct for
Since it is correct for B, there exist
not all zero such that for any
. We want to find scalars
. Try to see what happens if we let
Tonio: I think he has not reached the part of basis yet - this is why he is required to prove both claims... also, it is good practice to do so since he is only now starting with proofs!