Newbie vector spaces question So browsing the tasks our prof gave us to test our skills before the June finals, I've encountered something like this:
"Prove that the kernel and image are subspaces of the space V: $\ker(f) < V, \operatorname{im}(f) < V$, where $<$ means a subspace."
Is it just me or there's something wrong with the problem? I mean: I was rewriting the tasks from the blackboard by hand so I may have made a mistake but is a problem like this solvable or I messed up and should rather look for the task description from someone else? Cause for the time being, I don't see anything to prove here since we don't know what V is, right?

Implicit in the question is that $f:V\rightarrow V$ is a linear transformation from $V$ to $V$.  What you need to do in this problem is show that the kernel and image are not only subsets of $V$, but actually linear subspaces.  That is, you need to prove that they are closed under scalar multiplication and vector addition.
