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 Transformations and Basis

  1. Oct 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that if [tex]{ v_1, ... , v_k} [/tex] spans [tex] V [/tex] then [tex] {T(v_1), ... , T(v_k)}[/tex] spans [tex] T(v) [/tex]

    2. Relevant equations

    3. The attempt at a solution

    So we know that every vector in V can be written as a linear combination of [tex] v_1,...v_k [/tex] thus we only need to show that [tex] {T(v_1), ... , T(v_k)}[/tex] spans [tex] T(c_1v_1 + ... + c_kv_k) [/tex]

    However, I'm not sure how to do that.
  2. jcsd
  3. Oct 18, 2011 #2
    You probably meant to write T(V) here...

    What in earth does that even mean??????

    You need to show that [itex]\{T(v_1),...,T(v_k)\}[/itex] spans T(V). So take a vector in T(V) and show that it can be written as

    [tex]T(c_1v_1 + ... + c_kv_k) [/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Linear Transformations and Basis