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If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 ∩ V2 is _____.

1. 0
2. 1
3. 2
4. 3

Correct answer: 2

Solution

By the dimension formula dim(V1)+dim(V2)=dim(V1+V2)+dim(V1 cap V2). Since dim(V1+V2)<=6, we get dim(V1 cap V2)>=4+4-6=2. The smallest possible dimension is 2, not 1.

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