Answer:
See the proof below.
Explanation:
We can proof this with the following theorem "Let B a subset of a vector space of L then the span(B) is a subspace of L , and is the samlles subspace containing B"
Proof
We can show that the span(B) is a subspace of L.
For this special case we assume that
and for this case the
and we can see that B \subseteq M=span (B) [/tex]
In order to see that the span(B) is a subspace of L we can assume two elements let's say
we can write this like that:
For some vectors
\in B and scalars
in R
So then the linear combination r+s is defined as:
Let
a constant in R
So then we have all the conditions satisifed and we can conclude that M=span(B) is a subspace of L.