Khan Academy: Linear Algebra: Representing Vectors in Rn Using Subspace Members

A video lesson showing a series of proofs that culminate in explaining that any member of Rn can be represented as a unique sum of a member of some subspace of Rn and a member of its orthogonal complement. Ideas included in the proof are that the zero vector is the only vector in both a subspace and its orthogonal complement and all of the basis vectors in the subspace and its orthogonal complement are linearly independent and form a basis for Rn. [27:00]