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For instance, my book gives the following reason:

Transformation T is not isomoprhic because T((t-1)(t-3)) = T(t^2 - 4t +3) = zero vector.

I don't get why this means T is not an isomorphism. Can anyone explain?

PS. T is a transformation from P_2 to R^(3).

the actual T is: T(f(t)) =

f(1)

f'(2)

f(3)

Thanks.