I'm confused about the intersection of sub spaces. 1) If the intersection doesn't contain the origin then you can't multiply by zero and hence doesn't satisfy condition 22) v&w may be in both sub spaces and can be added or scalar multiplied in either, but once the subspace is constrained, how do you know this is still true?####[['intersection of sub spaces', 'Mathematical_Related_Concept', 'NEU'], ['v&w', 'Mathematical_Related_Concept', 'NEU'], ['intersection', 'Mathematical_Related_Concept', 'NEU'], ['origin', 'Mathematical_Related_Concept', 'NEU'], ['sub spaces', 'Mathematical_Related_Concept', 'NEU']]