Hi, Can a linear trans. T:V-->W be 1 to 1 if Ker(T) != {the zero vector on V}?
Last edited by jfk; Apr 24th 2012 at 03:07 AM.
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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.
In fact, if f(v)= 0 (for $\displaystyle v\ne 0$) if u- w= v then it is also true that f(u)= f(v).
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