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2. Let Let T: VW be a linear map. Let {₁,..., Un} be a list of n vectors in V. Prove that if the vectors U₁,..., Un are independent and T is injective, then T(v₁),...,T(vn) are also independent.

2. Let Let T: VW be a linear map. Let {₁,..., Un} be a list of n vectors in V. Prove that if the vectors U₁,..., Un are independent and T is injective, then T(v₁),...,T(vn) are also independent.

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2. Let Let TV → W be a linear map. Let {v₁,..., Un} be a list of n vectors in V. Prove that if the vectors v₁,..., Un are independent and T is injective, then T(v₁), ...,T(vn) are also independent.
Transcribed Image Text:2. Let Let TV → W be a linear map. Let {v₁,..., Un} be a list of n vectors in V. Prove that if the vectors v₁,..., Un are independent and T is injective, then T(v₁), ...,T(vn) are also independent.
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