# Question: kernel and image proofl inear algebrai dont understand the solution...

###### Question details

Kernel and image proofl inear algebraI don't understand the
solution **L(0v)=0w if i put L(v3)=0w is it ok or not why it
has to be L(0v)=0w?? is it because one to one 0 has to be mapped to
0???**

A linear transformation L: V → W is said to be

one-to-one if L (v1) = L (v2) implies that v1 = v2

(i.e., no two distinct vectors v1, v2 in V get mapped

into the same vector w ∈ W). Show that L is

one-to-one if and only if ker(L) = {0V }