SOLUTION: If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V?

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Question 1172394: If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V?
Answer by ikleyn(52775) About Me  (Show Source):
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If U and V are subspaces of a 7 dimensional vector space V, then what is the possible dimension of the intersection of U and V?
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As I see from your post, you use the letter  V  for both the space and subspace.

        What is it: an error or a mistake ?     Or   BOTH ?





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Comment from student:   Vector space is  X  and  U  and  V  are subspaces of  X.



My response : 

    Let  n be the dimension of subspace U,  n = dim(U);

    Let  m be the dimension of subspace V,  m = dim(V).


    Let  W be intersection of the linear subspaces U and V.


    Then W itself is the linear subspace, and its dimension d(W) can be any integer non-negative number


        d(W) <= min ( d(U), d(W) ).


    That is all what I can say/answer in response to the posed question.