Thread: Aother subset proof

Show that if S1 and S2 are arbitrary subsets of a vector space V, then span(S1 union S2) = Span(S1)+Span(S2).
Can someone solve this?

And did I approach this correctly

1. Let s1 and s2 be arbitrary subsets of a v. space V.
2. Let x be an arbitrary vector such that x belongs to (S1 union S2). So x belongs to S1 or x belongs to S2. Then Span(S1) IS all the linear combinations containing the vector x such that (for all a belonging to the field F)(a is a scalar) then the summation a*x belongs to Span(S1)
and then.....

my wordin prob sounds bad i dont know how u guys use the summation symbol and the for all symbol on the internet... how do u guys do that anyhow

Originally Posted by ruprotein

Show that if S1 and S2 are arbitrary subsets of a vector space V, then span(S1 union S2) = Span(S1)+Span(S2).
Can someone solve this?

Because the right hand side is the set of ordered paris of and .

Hence your probably mean to say (and you tell me what):
1)
2) .

By I mean, isomorphic.

Actually he does mean The term is only a union not a set of ordered pairs.

As for a proof, it is easy to see that .
To prove is just a messy exercise. In any linear combination from you need to separate the spanning elements into one of those two sets.