let $W$ be a subspace of vector space $V$. Prove that there exist a linear mapping $$L\colon V\to V$$ such that $$\ker(L)=W.$$
I have totally no idea how to proceed this, so you are very welcomed to give any hint. We just learned the four fundamental subspaces and the nullity theorem if that helps. Thanks in advance!
edit:yes,this question is under finite dimensional assumption.