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**1. The problem statement, all variables and given/known data**

Let ##T:V \rightarrow W## be an ismorphism. Let ##\{v_1, ..., v_k\}## be a subset of V. Prove that ##\{v_1, ..., v_k\}## is a linearly independent set if and only if ##\{T(v_1), ... , T(v_2)\}## is a linearly independent set.

**2. Relevant equations**

**3. The attempt at a solution**

##\rightarrow##: I began with the definition of linear independent vectors.

But I realized this could map to vectors that become dependent vectors in ##W##.

I suppose the fact that T is an isomorphism is a hint. Can anyone give me ideas?

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