Prove that if b=(p,) is any subset of a linear space l, then m=span b is a subspace of l.

See the proof below.

Step-by-step 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.