This may or may not be a totally stupid question. So let's see:

Suppose $S,T$ are two linear transformations between some fixed pair $V, V'$ of finite-dimensional real linear vector spaces. Now suppose further that $S,T$ have nontrivial kernels in $V$ and that the intersection of these kernels is, say, nontrivial.

Question: how can we choose a linear transformation $R=R(S,T):V \to V'$ such that $R$ has kernel exactly equal to the intersection of the kernels of $S,T$?

I think it's a funny question.