1. The problem statement, all variables and given/known data [itex]V[/itex] is a vector space with dimension n, [itex]U[/itex] and [itex]W[/itex] are two subspaces with dimension k and l. prove that if k+l > n then [itex]U \cap W[/itex] has dimension > 0 2. Relevant equations Grassmann's formula [itex]dim(U+W) = dim(U) + dim(W) - dim(U \cap W)[/itex] 3. The attempt at a solution Suppose k+l >n. Suppose that [itex]dim(U \cap W) \leq 0[/itex] since the dimension can't be negative [itex]dim(U \cap W) = 0[/itex] then Grassman formula reduces to [itex]dim(U+W) = dim(U) + dim(W)[/itex] [itex]dim(U+W) = k +l > n[/itex] this is a contraddiction because [itex]U+W[/itex] has dimension grater than the dimension of his enclosing space. is this a valid proof?