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Math Help - Linear Independence in linear transformations

  1. #1
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    Linear Independence in linear transformations

    Let V, W be two vector spaces, and F: VW a linear map. Let w1, ... wn be elements of W which are linearly independent, and let v1...vn be elements of V such that F(vi) = wi, for i = 1,...n. Show that v1,...vn are linearly independent.
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  2. #2
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    Quote Originally Posted by grandunification View Post
    Let V, W be two vector spaces, and F: VW a linear map. Let w1, ... wn be elements of W which are linearly independent, and let v1...vn be elements of V such that F(vi) = wi, for i = 1,...n. Show that v1,...vn are linearly independent.
    What is linear independence? If you assume that some set of coefficients and vectors in V are linearly dependent, what does that imply when you apply the transformation to W?
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