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!

Homework Help: Finding basis probelm

  1. Dec 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Let S be the form of (a, b,c ,d )in R4, given a not equal to 0. Find the basis that is subset of S.


    2. Relevant equations



    3. The attempt at a solution
    I got a(1,0,0,0), b(0,1,0,0), c(0,0,1,0), d(0,0,0,1) as basis. a not = 0
    But i wasn't sure what the significances of a not = to 0 means

    Any help would be appreciated.
    Thanks in advance.
     
  2. jcsd
  3. Dec 11, 2009 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It means find four elements of R4 that are linearly independent and all of whose first components are non-zero. That would comprise such a basis.
     
  4. Dec 12, 2009 #3

    HallsofIvy

    User Avatar
    Science Advisor

    However, the set of all (a, b, c, d) in R4 such that [itex]a\ne 0[/itex] is NOT a subspace and so does NOT have a basis. Are you sure you have read the problem correctly?
     
  5. Dec 12, 2009 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I'm thinking the OP may have the problem stated correctly since he/she calls S a set. They just seek a basis for R4 choosing only from that set.
     
  6. Dec 13, 2009 #5

    HallsofIvy

    User Avatar
    Science Advisor

    Ah! You are right. I misread it. The problem is NOT to find a basis for S but to find a basis for R4 such that the first component of each basis vector is not 0.
    I would be inclined to take the "standard" basis and change the first component of each to a simple non-zero number. Then check to see if they are still independent.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook