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Linear Transformations

  1. May 16, 2005 #1
    I've uploaded a document which I am currently working on. I would like to verify if I am doing these problems correctly. Thank you.

    In the first attachment (3.4b)
    For 1.
    a. 4x^3-2x
    b. T(P)=0
    ker T={C:C [tex]\in[/tex]R}
    Im T = {P|P is less than degree 3 or less}

    c. T is not one to one because P is a constant. T is not onto because it's degree less than 3. I am not sure if I am proving this right. I'd appreciate some help.

    For 2.
    a. 1/5x^5-1/3x^3+C
    b.
    ker T={C:C [tex]\in[/tex]R}
    Im T = {P|P is less than degree 5 or less}
    T is not one to one because C=0. But, T is on-to. How do I prove this?

    In the second attachment (3.4a) part 4.
    I proved that T is one to one because T(f)=T(g), f=g How do I prove that this is on-to?
     

    Attached Files:

  2. jcsd
  3. May 17, 2005 #2
    nvm, I understand it.
     
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