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A little help with Linear Transformations

  1. Oct 30, 2005 #1
    Okay, I will just admit that I stink at using mathematical proof in Linear. I hope someone can give me a push with this problem

    Prove that T : R(real)^3 -> R(real)^3 defined by T([yz,xz,zy]) is not a linear transformation.

    Reading my book I know that I need to prove that the transformation is closed under additivity and scalar multiplication, but alas I do not know where to begin with this. Any help would be appreciated.
     
  2. jcsd
  3. Oct 30, 2005 #2
    That's what you would do if you wanted to prove that T /was/ a linear transformation. You're asked to prove T is not a linear transformation. You can do this by exhibiting two vectors a, b such that T(a + b) != T(a) + T(b), for example.
     
  4. Nov 1, 2005 #3

    mathwonk

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    look, the whole idea of a, onear transformation is that when it is given in formulas, the formulas are linear, i.e. first degree. what degree are your formulas?
     
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