This is an old problemset question that I didn't managing to solve before the hand-in, and now I'm trying to understand how to solve it.
I'm trying to prove that for $L:V \rightarrow W$ that isormphism $V/W \cong K$ is true. From the question we know that $V=K\oplus W$. V is the domain, W is the image, and K is the kernel of L. I can relatively well prove the "regular" isormphism theorem, but I don't know how to proceed here. I'm starting with defining $T(v+W)$ but I don't know what to set it equal to, and from there how to prove that it is well-defined
Thanks!
EDIT: We are given that $V=K\oplus W$. If it also helps, one sub-part of the question before this one was also to show that x^2-x is the minimalpolynomial of L, but I don't know whether that is of any help in this problem