Question: Let L: V W be a linear transformation, and let S = {v1, v2,..., vn} be a set of vectors in V. Prove that

Let L: V → W be a linear transformation, and let S = {v1, v2,..., vn} be a set of vectors in V. Prove that if T = {L(v1), L(v2),..., L(vn)} is linearly independent, then so is S. What can we say about the converse?

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