Let V, W be two vector spaces, and F:V→W 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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- Sep 17th 2009, 03:51 PMgrandunificationLinear Independence in linear transformations
Let V, W be two vector spaces, and F:

*V*→*W 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.* - Sep 17th 2009, 04:22 PMJameson