(b) Proposition 1 Let T: V W be a one-to-one linear transformation of linear spaces V and W, suppose that a set of vectors (1, 2, 03} CV is linearly independent. Prove that {T(,), T(72),T(53)} CW is linearly independent. Below is a "proof" of the above proposition. In the spaces, fill in the missing parts to complete the proof or give your own proof. Proof: Suppose that a,T(,) + a2T(2) + a3T(3) 0. Then, since T is a linear transformation we get T( = 0. Since T is one-to-one, we get that ai01 + a202 + azu3 = Since (, 02, s} is a linearly independent set we get that Thus (T(),T(72), T(03)} CW is linearly independent.

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