Consider the plane ax+by+cz=0

1) Describe how you would use the SVD to find orthogonal basis vectors for the plane.

2) How many basis vectors are required to express a point on the plane?

3) Find the point on the plane that is closest to (,,) -- note that this corresponds to an orthogonal projection onto the plane.

Hint: How can we express this problem in terms of projection onto an ortho-complement of a subspace of a matrix A?