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Is an unspecified matrix invertible?

  1. Jan 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Let T be the unique linear operator on C3 for which [tex] T_{\epsilon1}=(1,0,i), T_{\epsilon2}=(0,1,1), T_{\epsilon3}=(i,1,0).
    [/tex]
    Is T invertible?
    2. Relevant equations
    If we show T is non singular or T is onto, then this would imply T is invertible.

    3. The attempt at a solution
    I don't really know where to start, I thought about trying to brute force solve the matrix T but I am quite sure there is a more elegant way and hoping someone can give me a kick in that direction.
     
  2. jcsd
  3. Jan 21, 2015 #2

    Stephen Tashi

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    Assuming the scalars for this vector space are the complex numbers, I think [itex] Te_1 [/itex] is a linear combination of [itex] Te_2 [/itex] and [itex] Te_3 [/itex]. If that's correct then you can show that T maps a 3-D space to a 2-D space.
     
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