Show that if u has a unit length, then the rank-1 matrix P=uu^t is a projection matrix, meaning P^2=P and P^t=P. By choosing u = a / ||a||, P becomes the projection onto the line through a, and Pb is the point p = xa. Rank-1 projections correspond exactly to a least squares problem in 1 unknown.
OK... I don't really know what they're talking about... The only relevant equation I have is P=A(A^tA)^-1A^t. I don't know how to apply it. Please help!