My book has an exercise:
"Suppose that $W$ is a subspace of a finite-dimensional vector space $V$.
a) Prove that there exists a subspace $W'$ and a function $T:V\longrightarrow V$ such that $T$ is a projection on $W$ along $W'$
b) Give an example of a subspace $W$ of a vector space $V$ such that there are two projections on W along two (distinct) subspaces."
Do I understand this right, that in a) $W'$ is supposed to be a subspace of $V$, not of $W$, and that in b) two distinct subspaces of $V$, not $W$ are meant?