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Element of a vector group (subset?)

  1. Oct 11, 2015 #1
    • Member warned about posting with no effort shown
    EDIT: I think i screwed up and posted in the wrong section. Sorry. Should i make a new one to the correct place? Can this one be moved?

    Hello. I have a couple of problems here, that i will have to translate from another language, so im not 100% sure if im using the correct terms.

    (1) Let u, v, w ∈ ℝn be vectors. Find out if the vector u+v is an element of the group (subset?) (2u-v, 2u-w, 2w-u).

    (2) Show that the ℝn vectors u=(a,1,-1), v=(b,-1,2) and w=(c,1,3) are linearly dependant exactly when c-4b-5a=0.

    So, i dont know what to do with these.
     
    Last edited: Oct 11, 2015
  2. jcsd
  3. Oct 11, 2015 #2

    Svein

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    In (2) it seems to me that you are talking about vectors in ℝ3. This observation should make that problem easier.

    In (1) you must check if there are scalars a, b and c such that a⋅(2u-v)+b⋅(2u-w)+c⋅(2w-u)=u+v.
     
  4. Oct 11, 2015 #3
    Thank you for answering! For (2), that is a typo, it's supposed to say ℝ3. I still dont quite understand what im supposed to do.
     
  5. Oct 11, 2015 #4

    Svein

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    Again, it is a question regarding a set of equations. You have three equations with three unknowns - for what values of a, b , c is there no solution?
     
  6. Oct 11, 2015 #5
    Dont i have 4 equations and 6 unknowns? The scalars and a,b and c?
     
  7. Oct 11, 2015 #6

    Svein

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  8. Oct 11, 2015 #7
    I hadn't heard of it, and i haven't learned determinant yet, either :F
     
  9. Oct 11, 2015 #8
    So here are my attempts:
    (1) https://dl.dropboxusercontent.com/u/34732003/h/20151011_220232.jpg [Broken]
    I stopped, because i wasnt sure what i was doing and it felt like nonsense.

    (2) https://dl.dropboxusercontent.com/u/34732003/h/20151011_220130.jpg [Broken]
    Numbers show the order in which i did things. 1 and 2 seemed like things i could do, then i started the matrix and realised i had no idea what to do with the a, b and c. Then, i moved on to 4 to see if i anything new and interesting showed up by mixing and matching the equations. It didnt. (Now i realise they're not all supposed to equal 0, as they are L.dependent.)
     
    Last edited by a moderator: May 7, 2017
  10. Oct 11, 2015 #9

    Mark44

    Staff: Mentor

    Please post your attempts here, rather than as images on dropbox. Everything you have done can be done using either BBcodes or LaTeX. We have tutorials on each of these types of markup.
    LaTeX: https://www.physicsforums.com/help/latexhelp/
    BBcodes: https://www.physicsforums.com/help/bb-codes

    Both can be accessed from INFO --> Help/How-To
     
    Last edited by a moderator: May 7, 2017
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