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Math Help - linear transformation

  1. #1
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    linear transformation

    Determine a linear transformation T:V2->V2 , which maps all the vectors on the line x+y = 0 onto thmeselves (T is not I).
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  2. #2
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    Quote Originally Posted by reha View Post
    Determine a linear transformation T:V2->V2 , which maps all the vectors on the line x+y = 0 onto thmeselves (T is not I).

    x+y=0\Longleftrightarrow y=-x\Longleftrightarrow the vector (1,-1) , generator of the above line, must be mapped either to himself or to another vector in the same line, so you can try T(x,y):=(y,x) . Now check T is a lin. trans. and it maps the above line to itself.

    Tonio
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