If V1 and V2 are 6 dimensional subspaces of a 10 dimensional vector space V, what is the smallest possible dimension that V1 intersection V2 can have ?
A) 0
B) 1
C) 2
D) 4
E) 6
EugeneKudashev wrote:take two 6-dimensional vectors and look at their intersection. it is plain that it contains no less than 2 components.
EugeneKudashev wrote:perhaps I'll sketch it like that:
| | | | | | x x x x
x x x x | | | | | |
1 2 3 4 5 6 7 8 9 10
first row is your first subspace ( | stands for element, x for emptiness) and the second row is your second subspace. both have dim=6 and as you can see their intersection should not "exceed" dim=10. thus, intersection has dim no less than 2. I hope that is understandable.
Hom wrote:Hi, i was thinking the same way at first but then I came up with another thought. Not sure if it's valid.
Let a 2D plane p1 to be x=0, and the other plane p2 to be x=2. See p1 and p2 are 2D space of 3D space. But there is no intersection between p1 and p2.
Please comment.
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