Question

let a be a fixed nonzero vector in R^2. a mapping of the form

L(x) = x +a
is called a translation. show that a translation is not a linear operator. Illustrate geometrically the effect of a translation.

Answer 1

i linear operation i believe is where: L(x+a) = L(x) + L(a)

Answer 2

but without knowing the context of your material its hard for me to say

Answer 3

so i just have to prove that addition and multiplication work for the given L(x) = x+a then?