Suppose U and W are both 4-dimensional subspaces of C6. Prove that there exist two vectors in U∩W such that neither of these vectors is a scalar multiple of the other.
By 2.43
dim(U∩W)=dimU+dimW−dim(U+W)=8−dim(U+W)≥2
Therefor we can find two independent vectors v1,v2∈U∩W which clearly won't be scalar multiples of eachother.