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 a basis for vector spaces

  1. Apr 10, 2008 #1
    I'm having trouble finding a basis for algebraically defined vector spaces where there is more than one condition. For instance, I can easily find a basis for the vector space in R^3 defined by a+2b+3c=0 (where a,b,c are the elements of the vector), but I have no idea what to do when the vector space is defined by something like a-b-c=0 & 2a+3b+8c=0.

    For the first example I would write that every vector in the space has to be of the form (-2b-3c, b, c) = b(-2,1,0) + c(-3,0,1), so a basis for the vector space would be {(-2,1,0),(-3,0,1)}. I have no idea what to do for the second example.
  2. jcsd
  3. Apr 10, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    You got to (-2b-3c, b, c) by just algebraically eliminating a. Now b and c are free variables. For the second case do the same thing, but eliminate two variables. So the result is, say, (k1*c,k2*c,k3*c). Then the basis is {(k1,k2,k3)}.
  4. Apr 11, 2008 #3


    User Avatar
    Science Advisor

    Dang! I wrote out a brilliant explanation, then went back and read Dick's. His was better!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook