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Math Help - Invertible Linear Maps

  1. #1
    Junior Member
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    Invertible Linear Maps

    Let L: R3 to R3.

    Show that L(x,y,z) = (x-y,x+z,x+y+2z) is invertible. We have been using the theorem that if the KerL is {0} and L is surjective then the map is invertible. But in this case the KerL is not {0}, for example take L(1,1,-1) = (0,0,0). So I don't get it.
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  2. #2
    Super Member
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    This map is not invertible. For e.g. (0,0,1) has no inverse.
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