Exercises on projections onto subspaces
Problem 15.1: (4.2 #13. Introduction to Linear Algebra: Strang) Suppose A is the four by four identity matrix with its last column removed; A is four by three. Project b = (1, 2, 3, 4) onto the column space of A. What shape is the projection matrix P and what is P?
Problem 15.2: (4.2 #17.) If P2 = P, show that (I − P)2 = I − P. For the matrices A and P from the previous question, P projects onto the column space of A and I − P projects onto the .
