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Homework Help: Linear transformation - adding and subtracting?

  1. Jan 17, 2008 #1
    [SOLVED] Linear transformation - adding and subtracting?

    1. The problem statement, all variables and given/known data

    Suppose T : P2 -> P2 is a linear transformation satisfying T(3 − x + 4x^2) = 1 + x − x^2 and
    T(2 − 3x + 2x^2) = 7 + 3x + 2x^2.
    Find T(7x + 2x^2).

    3. The attempt at a solution

    First of all, it's linear. To find T(2x^2), I can say -x^2-2x^2 = -3x^2 = T(2x^2)? And similarily for T(7x)?
  2. jcsd
  3. Jan 17, 2008 #2
    No wait, I solved it.. I can't do what I did in my original post.

    I have to solve a linear system of equations to find T(7x + 2x^2) written from T(3 − x + 4x^2) and T(2 − 3x + 2x^2).

    Bottom line is, I solved it.
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