We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spaces lp,1p< and c0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator from lp,1p< or c0 onto anyone of their maximal proper subspaces.