[Solved] 18.06 Unit 2 Exercise 2-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 .