1. The problem statement, all variables and given/known data Give an example of a subspace W of a vector space V such that there are two projections on W along two distinct subspaces. 2. Relevant equations 3. The attempt at a solution I tried looking into Euclidean geometry spaces (R3 and R2) but no matter what subspace W I choose, there is only one subspace along which W projects. For example, if my vector space is (x,y,z) and my subspace W is (x,y,0), then by the properties of subspaces in projection, the other subspace must be (0,0,z). How is it possible to get two distinct subspaces along which W projects, and still have a direct sum of the same vector space?