Exercise 5.6.4 If {V₁, ···,Vr} is linearly independent and T is a one to one linear transformation, show that {TV₁,,Tvr} is also linearly independent. Give an example which shows that if T is only linear, it can happen that, although {V₁,,Vr} is linearly independent, {TV₁,,Tvr} is not. In fact, show that it can happen that each of the Tv; equals 0.

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