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Linear transformations

  1. Sep 10, 2009 #1
    Hi

    I am trying to do a math assignment and I am finding it really difficult.

    Assume you have a linear transformation from T: P3(R) --> R4

    What relevance is there to applying the transformation to the basis elements of P3(R), ie: T(1), T(x), T(x^2), T(x^3)? Why is this subset special? How does it help determine the range of T?

    Thanks.
     
  2. jcsd
  3. Sep 10, 2009 #2
    [itex]dim(P^3)=dim(\mahtbb{R}^4)=4[/itex]

    you have the basis elements of [itex]P^3[/itex].

    The action of T on each of these basis elements will let you know the basis elements of [itex]\mathbb{R}^4[/itex]

    i.e. [itex]1,x,x^2,x^3[/itex] are the basis elements of [itex]P^3[/itex]
    and [itex]T(1),T(x),T(X^2),T(x^3)[/itex] are the basis elemetns of [itex]\mathbb{R}^4[/itex]

    applying T to any element of [itex]p(x) \in P^3[/itex] will yield [itex]T(p(x)) \in \mathbb{R}^4[/itex] and [itex]T(p(x))=aT(1)+bT(x)+cT(x^2)+dT(x^3)[/itex] where [itex]a,b,c,d \in \mathbb{Z}[/itex]
     
  4. Sep 10, 2009 #3
    thank you!
     
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