Let $f,f_1,f_2$ be linear functionals on vector space V (infinite dimensional) and $\ker f\supset \ker f_1\cap \ker f_2$. I want to obtain that $f\in \operatorname{span}\{f_1,f_2\}$.
I tried to use factors, but i don't think that $V/\ker f \subset V/(\ker rf_1 \cap \ker f_2)$...
Another approach is to find vectors $y, z$ s.t. $\forall x\ f(x-yf_1(x)-zf_2(x))=0$, but it didn't work out for me.
Any hints?