Prove T([yz,xz,zy]) is not a linear transformation

[Rounder01]

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.

 

[Muzza]

Reading my book I know that I need to prove that the transformation is closed under additivity and scalar multiplication, ...

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.

 

[mathwonk]

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?