# Math Help - About 1-1 Linear Transformations

1. ## About 1-1 Linear Transformations

Hi,
Can a linear trans. T:V-->W be 1 to 1 if Ker(T) != {the zero vector on V}?

2. ## Re: About 1-1 Linear Transformations

If v ∈ Ker(T) where v ≠ 0, then T(v) = T(0) = 0, so...

By the way, the question should probably say, "Ker(T) != {the zero vector on V}" because Ker(T) ⊆ V.

3. ## Re: About 1-1 Linear Transformations

In fact, if f(v)= 0 (for $v\ne 0$) if u- w= v then it is also true that f(u)= f(v).