Proposition 1: Let T: V-> W be a linear transformation of linear spaces V and W, suppose that a set of vectors }} CV has the property that Tví TV3 )} :{T (₁²), T (₂²), T 12,03 } . CV is linearly independent. {0₁ →→ V1, V2, V3 independent. Then, the set of vectors →→ V1, V2, V3 Below is a "proof" of the above proposition. You may use it as a template and upload your proof below. →> → →>> Proof: Suppose that a₁v₁ + a2v₂ + a3v3 = Ō. Then, applying T to both sides we get Since T is a linear transformation, we get Since {T(v²), T (√₂²),T (v₂)} CW is linearly are linear independent we get that

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