Let L be a function that follows the definition and L0 it's homogeneous identical.
(-0.5)[(1,-2,-1)-(1,-2,1)] = (0,0,1) solves L0 ==>
(1,-2,-1)+(0,0,1) = (1,-2,0) solves L ==>
(-2)[(1,-4,0)-(1,-2,0)] = (0,4,0) solves L0 ==>
(1,-4,0)+(0,4,0) = (1,0,0) solves L

Therefor, (1,0,0) can't be a solution to L0, since L isn't homogeneous.