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Linear transformation one-to-one

  1. Oct 6, 2014 #1
    1. The problem statement, all variables and given/known data
    let ##T:\mathbb{R^3} \rightarrow \mathbb{R^3}## where ##T<x,y,z>=<x-2z,y+z,x+2y>##

    Is T one-to-one and is the range of T ##\mathbb{R^3}##?




    3. The attempt at a solution

    I took the standard matrix A ##\left[\begin{array}{cc}1&0&-2\\0&1&1\\1&2&0\end{array}\right]##

    det(A)=0 so by equivalence T is not one-to-one and by equivlence again the range is not ##\mathbb{R^3}##
     
  2. jcsd
  3. Oct 6, 2014 #2

    LCKurtz

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    What is your question?
     
  4. Oct 6, 2014 #3
    is that correct?
     
  5. Oct 6, 2014 #4

    LCKurtz

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    I suspect you already know the answer is yes.
     
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