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**Prove that if s1 and s2 are subsets of a vectorspaceV such that....**

## Homework Statement

Prove that if s1 and s2 are subsets of a vector space V such that S1 is a subset of S2,then span(S1) is a subset of span(s2). In particular, if s1 is a subset of s2 and span(s1)=V, deduce that span(s2)=V.

## Homework Equations

## The Attempt at a Solution

I came up with this, but I doubt its right. Particularly, it only applies to a finite subset. I don't know how I'd modify it to fit any subset.

Let s1,s2 be subsets of V such that s1 is a subset of s2. In cases1=s2, it is clear that span(s1)=span(s2). In case s1 does not equal s2, let x1...xn be the elements of s1. Then a1x1+a2x2+....anxn for all scalars A are in span(s1). We can write x1....xn....xk as the elements of s2. Then by definition a1x1+...anxn+....akxk are in span(s2). So span(s1) is a subset of span(s2).

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