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

  1. Oct 6, 2013 #1
    1. Give information
    Let T: P3 ---> P3 be the linear transformation described by:
    Find the matrix of T with respect to the standard basis b {1,x,x^2,x^3}.

    3. The attempt at a solution
    I found the transformations on the standard basis b:
    T(1) = 2
    T(x) = 3
    T(x^2) = 2x^2 -2x +5
    T(x^3) = 9x^2 - 9x + 9
    I am confused on what to do next...
  2. jcsd
  3. Oct 6, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Write your functions so they look a little more like vectors, write a+bx+cx^2+dx^3 as the column vector [a,b,c,d]. So T(1)=2 becomes T([1,0,0,0])=[2,0,0,0]. Does that help?
  4. Oct 6, 2013 #3
    Ok, then I should find T(1,0,0,0), T(0,1,0,0), T(0,0,1,0) and T(0,0,0,1) right?
  5. Oct 6, 2013 #4


    User Avatar
    Science Advisor
    Homework Helper

    Right. You really already did. Just write them as column vectors. Then those will be the columns of your matrix.
  6. Oct 6, 2013 #5
    Okay thank you very much for your help =)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Linear transformations
  1. Linear transformation (Replies: 11)

  2. Linear Transformation (Replies: 1)

  3. Linear transformation (Replies: 4)

  4. Linear transformation (Replies: 18)