1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra span proof

  1. Mar 7, 2013 #1
    1. The problem statement, all variables and given/known data
    [tex] S_1 [/tex] and [tex] S_2 [/tex] are subsets of a vector space. When is this:[tex] span(S_1 \cap S_2) = span(S_1) \cap span(S_2) [/tex] true? Prove it.


    2. Relevant equations



    3. The attempt at a solution
    conjecture: iff the two subsets are vector spaces.
     
    Last edited: Mar 7, 2013
  2. jcsd
  3. Mar 7, 2013 #2

    Zondrina

    User Avatar
    Homework Helper

    It's true when both sides are subsets of each other.

    Choose an arbitrary element in each set and show it belongs to the other set both ways.
     
  4. Mar 7, 2013 #3
    sorry, but that is of no help. I am asking for a condition and a proof for "iff".
     
  5. Mar 7, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Well, what do you know and what have you tried? Do you know what "span" means?

    Or do you just want someone to do the problem for you?
     
  6. Mar 7, 2013 #5
    ok. plz delete this post.
     
  7. Mar 7, 2013 #6

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's easy to see that your guess is wrong. Let ##\{e_1,e_2\}## be the standard basis of ##\mathbb R^2##. Let ##S_1=\{e_1\}## and ##S_2=\{e_1,e_2\}##. We have $$\operatorname{span}S_1\cap\operatorname{span} S_2 =\operatorname{span}(S_1\cap S_2)$$ but neither ##S_1## nor ##S_2## is a subspace.

    You will have to put in some effort of your own if you want help with the problem. In particular, you should include the definition of "span". Is ##\operatorname{span}\emptyset## defined?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Linear algebra span proof
Loading...