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?

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(52781) (Show Source): You can put this solution on YOUR website!
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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.

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