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Homework Help: There is a linear transformation from P1 to P1

  1. Aug 24, 2010 #1
    1. The problem statement, all variables and given/known data
    There is a linear transformation T from P1 to P1 where P1 is the set of all polynomials of degree at least 1.
    T(1 + 2x) = 2 + 4x and T(4 + 7x) = -2 + 2x

    Find T(-3 - 5x).


    2. Relevant equations
    T(1 + 2x) = 2 + 4x
    T(4 + 7x) = -2 + 2x

    3. The attempt at a solution
    Basis B1 = [1, 2] [4, 7]
    Basis B2 = [2, 4] [-2, 2]

    [-3, -5] in terms of Basis 1 = [1, -1], bring that into Basis 1 gives you 1*[2, 4x] + -1*[-2, 2x] = [0, 6x]

    The answer is not 6x.
     
  2. jcsd
  3. Aug 24, 2010 #2

    Dick

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    Why do you think 1*[2, 4x] + -1*[-2, 2x] = [0, 6x]? That doesn't look at all right.
     
  4. Aug 25, 2010 #3
    Haven't slept in 3 days, the other day, I was trying to calculate the cross product of two vectors in R5. What's worse, is I ended up with an answer.


    Close this, the answer's 4 + 2x.
     
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