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.
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.
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?