Proving Nonzero Vector Intersection in 3D Subspaces of R5

[RyanV]

Homework Statement

Prove that if V and W are three dimensional subspaces of R⁵, then V and W must have a nonzero vector in common.

Homework Equations

NA

The Attempt at a Solution

I've attempted to set up the problem by writing out,

V = { (1, 0, 0, 0, 0), (0, 1, 0, 0, 0), (0, 0, 1, 0, 0) }
W = { (0, 0, 0, 1, 0), (0, 0, 0, 0, 1), (1, 1, 0, 0, 0) }

After that, I'm lost.

I don't really like vector spaces because I don't understand it very well. So could whoever explain please explain thoroughly? =P I would help a lot because I want to know what's going on! hehe, thanks in advance =)

 

[lanedance]

rather than narrowing in on a single case, think aobut linear independence... what is the maximal number of linearly independent vectors, in any subspace of R^3?

similarly, how many vectors are in a the basis for R^5?