This video shows that, for any b that is in the column space of A, there is a unique member of the row space that is the "smallest" solution to Ax=b.

A video lesson illustrating that the orthogonal complement of the nullspace is equal to the row space and vice versa.

This video shows that any member of Rn can be represented as a unique sum of a vector in subspace V and a vector in the orthogonal complement of V.

An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...

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...

A video proving that the orthogonal complement of the orthogonal complement of some subspace V must be a member of the original subspace V.

Showing that if V is a subspace of Rn, then dim(V) + dim(V's orthogonal complement) = n