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.

Printable View

- September 17th 2009, 04:51 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.* - September 17th 2009, 05:22 PMJameson