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

such that

. 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!