Let $f$ be a map $\mathbb R^n\to\mathbb R$, $f(x)=|x_1|+\cdots+|x_r|-|x_{r+1}|-\cdots-|x_{r+s}|,\forall x=(x_1,\cdots,x_n)\in\mathbb R^n$ with $r\geq s\geq0,r+s\leq n$. Let $W_1,W_2$ be two subspaces of dimension $n-r$ satisfying $f(x)=0,\forall x\in W_1\cup W_2$. Show that $\dim(W_1\cap W_2)\geq n-(r+s)$.
For this problem, there is a hint that try to show that the dimension of the mininal subspace $W$ satisfying $f(W)=0$ is $n-(r+s)$. But I don't know how to prove this.