1. Let TR → Rm be a linear transformation, and let {V₁, V2, V3} be a linearly dependent set in Rn. Explain why the set {T(v₁), T(v₂), T(v3)} in Rm must also be linearly dependent. Remark: You argument should not be a "proof by example," that is, the argument should hold for arbitrary linear transformation T and arbitrary linearly dependent set of vectors {V1, V2, V3} in Rn.

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