Mathematics, 27.12.2019 05:31 holaadios222lol
Show that if s1 and s2 are subsets of a vector space v such that s1 c s2 then span(s1) c span(s2). in particular, if s1 c s2 then span(s1)
Answers: 3
. Then, we can write x as a linear combination of elements of s1, that is, there exist 
and 
such that 
. Now, 
then for all 
we have that 
. In particular, taking 
with 
we have that 
. Then, x is a linear combination of vectors in S2, therefore 
. We conclude that 
.
then reversing the roles of S1 and S2 in the previous proof, 
. Then 
, therefore 
.
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Show that if s1 and s2 are subsets of a vector space v such that s1 c s2 then span(s1) c span(s2). i...
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