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Linear transformations

  1. Oct 6, 2013 #1
    1. Give information
    Let T: P3 ---> P3 be the linear transformation described by:
    T(p(x))=p(x+1)+p(2-x).
    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

    Dick

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    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

    Dick

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    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 =)
     
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