Khan Academy: Linear Algebra: Orthogonal Complements as Subspaces

Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null space is orthogonal to every member of the row space, or that the null space is a subset of the orthogonal complement of the subspace, and also that the orthogonal complement is a subset of the null space. Uses that to show that the left nullspace of a matrix is the orthogonal complement of its column space. [22:08]