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Suppose that $T: \mathbb{R}^m \to \mathbb{R}^n$ is a linear transformation and that $v_1, v_2, \ldots, v_p$ are vectors in $\mathbb{R}^m$.

If $W = \{T(v_1), T(v_2), \ldots, T(v_p)\}$ is linearly independent in $\mathbb{R}^n$, does it follow that $S = \{v_1, v_2, \ldots, v_p\}$ is linearly independent in $\mathbb{R}^m$? Justify your answer with either a proof or a counterexample.

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    Maybe people will answer if you **ask politely**, instead of commanding them.2011-03-15
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    That is: Instead of copying your assignment onto the website and writing in the imperative, try *asking*. Especially, try to say what you have tried, and where (and why) you are stuck.2011-03-16

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