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Arr Lin. algebra problem (frustrating)

  1. Mar 26, 2006 #1
    the question asks;
    Consider the following matrices. What is the corresponding transfrmation on polynomials? Indicate the domain P_i and the codomain p_j
    The matrix is: [1,1;1,-1]
    I looked at the sol. manual and it states
    T(ax+b)=(a+b)x+(a-b)
    I seriously have no idea how they came up with that. I read the section and i don't see any examples on how to do it.
     
  2. jcsd
  3. Mar 26, 2006 #2
    Given an arbitrary polynomial [itex]ax+b \epsilon P_1(\mathbb{R})[/itex], what is its coordinate vector with respect to the standard ordered basis for [itex]P_1(\mathbb{R})[/itex]?

    What is the result when you multiply this coordinate vector (on the left) by your matrix?

    What is the element of [itex]P_1(\mathbb{R})[/itex] that corresponds to this result?
     
    Last edited: Mar 26, 2006
  4. Mar 26, 2006 #3
    the first line should be [itex]ax+b \ \epsilon \ P_1(\mathbb{R})[/itex]. For some reason the symbol [itex]\epsilon[/itex] isn't showing.
     
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