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Linear transformation defined by T(a + bx) = (a, a+b)

  1. Apr 1, 2009 #1
    Example
    Let T: [tex]P_1(R) --> R^2[/tex] be the linear transformation defined by T(a + bx) = (a, a+b).
    The reader can verify directly that T-1: [tex]R^2 --> P_1(R)[/tex] is defined by T-1(c, d) = c + (d-c)x. Observe that T-1 is also linear.

    I am reading my text and it kind of makes sense, but I have no clue how to verify what has been said above. It make sense to reverse everything, and because after the reversal since the inverse doesn't have the element c for the second element in the order pair for [tex]R^2[/tex] then we subtract it from the image of T-1? But I don't feel comfortable with the concept (of this reversal-and subtraction), and I don't know how to verify what has been said.
     
  2. jcsd
  3. Apr 1, 2009 #2
    Re: Invertibility

    If (c, d) is an element of the range of T (and thus the domain of T-1), then c = a and d = a+b for some element (a + bx) in the domain of T. This should start you in the right direction.
     
  4. Apr 1, 2009 #3
    Re: Invertibility

    Thank you,

    JL
     
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