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Find matrix of the linear function

  1. Mar 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the linear function F : P4 -> R5
    that sends the basis {1,x,x2,x3,x4} of P4 to the basis {e1,e1,e3,e4,e5} in R5, in that order , that is F(xn)= e(n+1)).
    (a) Is this function an isomorphism?
    (b) Consider the linear function D : P4-> P4
    p(x)->p'(x)

    Find the matrix of the linear function T : R5-> R5 such that
    (T o F)p(x) = (F o D)p(x)


    2. Relevant equations



    3. The attempt at a solution

    I solved for part a, but i have no idea how to start on part b
     
    Last edited: Mar 5, 2012
  2. jcsd
  3. Mar 5, 2012 #2

    tiny-tim

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    hi junsugal! :smile:

    (try using the X2 button just above the Reply box :wink:)

    do it for each basis element separately

    start with x4

    what do you get? :smile:
     
  4. Mar 5, 2012 #3
    hmm, what do you mean by start with x4?

    For part(a) I said that yes the function is isomorphic because P4 and R5 both have dimension of 5. And according to one of the properties of isomorphic, the dimensions of 2 vector spaces should be the same.

    Thanks for the tips! :)
     
  5. Mar 5, 2012 #4

    tiny-tim

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    put x = x4 in (T o F)p(x) = (F o D)p(x) :smile:

    (and your (a) is ok)
     
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