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Determine whether the linear transformation T is one-to-one

  1. Jul 13, 2011 #1
    Determine whether the linear transformation T is one-to-one

    a) T:P2 --> P3, where T(a+a1x+a2x^2)=x(a+a1x+a2x^2)

    b) T:P2 --> P2, where T(p(x))=p(x+1)

    I'm having difficulty because my teacher never showed examples like this one.
    Please help me on the procedure and solution.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 13, 2011 #2

    micromass

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    Hi hannahlu92! :smile:

    Showing that an operator T is one-to-one is equivalent to showing that the kernel is 0. So, what you must show is that

    [tex]T(a+bX+cX)=0[/tex]

    then a=b=c=0. Can you do that??
     
  4. Jul 13, 2011 #3

    Hurkyl

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    So what if the problem looks different? Why can't you solve the problem the way you would normally do?

    (Actually, it's probably easier to solve these problems than others you have faced, since there are easier ways than using your knowledge of linear algebra)
     
  5. Jul 13, 2011 #4
    I don't know how to because I haven't done one before. My teacher writes definitions on the board and proofs, but no practical examples, so nothing is cementing in my brain.
     
  6. Jul 13, 2011 #5

    micromass

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    Certainly you don't need any practical examples to figure out when

    [tex]T(a+bX+cX^2)=0[/tex]

    Just use the definition of T...
     
  7. Jul 13, 2011 #6
    In this case, proofs themselves are practical examples. That's the point of math courses.
     
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