Union and Sum of Subspaces

  • Thread starter nsj
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  • #1
nsj
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If U, U ′ are subspaces of V , then the union U ∪ U ′ is almost never a subspace (unless one happens to be contained in the other). Prove that, if W is a subspace, and U ∪ U ′ ⊂ W , then U + U ′ ⊂ W .

This seems fairly simple, but I am stuck on how to go about proving it.
 

Answers and Replies

  • #2
Deveno
Science Advisor
908
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use the closure properties of a subspace.
 
  • #3
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or you could ask your TA during office hours, Wildcat
 
  • #4
Deveno
Science Advisor
908
6
if W is a subspace, then for any w1,w2 in W, w1+w2 is also in W.

now, if u is U, and u' is in U', can we say these are in W? why?
 
  • #5
7
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gimme ur mail id,i will send da pics frm my book...this prove is in my syllabus...
 
  • #6
371
1
you know that adding two things from U is okay, you know that adding two things from U' is okay; what happens when you add something from U and something from U'? We already know that W is supposed to be a subspace. What is the definition of the subspace U + U'?
 

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