Linear Transformation

Probability Level 3

True or false :

Let T : R 3 → R 3 T: \mathbb R^3 \to \mathbb R^3 be defined by T ( x , y , z ) = ( x + 2 y − z , y + z , x + y − 2 z ) T(x,y,z) = (x+2y-z,y+z, x+y-2z) , then this linear transformation is injective.

False True

Jose Sacramento by Jose Sacramento , 66, Portugal

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1 solution

Otto Bretscher
Feb 28, 2016

T ( 0 , 0 , 0 ) = T ( 3 , − 1 , 1 ) = ( 0 , 0 , 0 ) T(0,0,0)=T(3,-1,1)=(0,0,0) , so that T T fails to be injective.

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