If {~v1,··· ,~vr} is linearly independent and T is a one to one linear transformation, show that {T~v1,··· ,T~vr} 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, {T~v1,··· ,T~vr} is not

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