Dimension Problem

Geometry Level pending

Let V be a vector space over the field K of dimension n, and let W1, W2 be 2 subspaces of V of dimensions m & n-m+p respectively, beign n,m,p>0. Prove that W1 ∩W2 $\ne$ {0}. Calculate the dimension of W1 ∩W2

n-m+p n+p-k whit p<k<n n+m-p p 0 m n