1. Not finding help here? Sign up for a free 30min 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!

Subspace of P3, linearly independence?

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Let U be the subspace of P3(ℝ) spanned by
    E={x^3,x^3-x^2,x^3+x^2,x^3-1}
    find a linearly independent subset F of E spanning U.


    2. Relevant equations
    E={x^3,x^3-x^2,x^3+x^2,x^3-1}


    3. The attempt at a solution
    a(x^3)+b(x^3-x^2)+c(x^3+x^2)+d(x^3-1)=0x^3+0x^2+0x+0
    (a+b+c+d)x^3+(-b+c)x^2+(-d)=0x^3+0x^2+0x+0

    a+b+c+d=0
    -b+c=0
    -d=0

    a=-2b, b=c, d=0
    t(-2,1,1,0), t[itex]\in[/itex]ℝ

    How do I figure out which vectors are linearly independent??
     
  2. jcsd
  3. Dec 14, 2011 #2
    Just say that P^3 is isomorphic to R^4 and then convert those vectors into a corresponding matrix and row reduce and your pivotal columns will tell you what vectors are linearly independent.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Subspace of P3, linearly independence?
  1. Independent subspace (Replies: 3)

  2. Linear independence (Replies: 3)

Loading...