Can two subspaces have vectors in common

[brru25]

Homework Statement

Can two 4-dimensional subspaces of F⁶₂ have exactly 9 vectors in common? Can they have exactly 8 vectors in common?

F⁶₂ is the 6-dimensional field where each (a₁, a₂, a₃, a₄, a₅, a₆) is an element of F₂.

The Attempt at a Solution

F⁶₂ obviously has 2⁶ = 64 elements. I want to say that if each of the 4 vectors in both subspaces are the same, then there can be up to that are also the same, which would mean that 9 isn't possible, but I don't think that's right at all.

Thank you ahead of time for your help.

 

[HallsofIvy]

Well, if two subspace has any vectors in common, then they have the subspace spanned by those vector in common. How many vectors does a one-dimensional subspace contain?

 

[brru25]

Well, if two subspace has any vectors in common, then they have the subspace spanned by those vector in common. How many vectors does a one-dimensional subspace contain?

Just one (I would think)??