2. Problem 2: (a) Suppose P E R""" is matrix satisfying the following two properties: i. P2 = F ii. PT = P Prove that for an},r vector b E R", the vector Pb E R" is the orthogonal projection of b onto the range space of P (denoted by R(P)) , i.e., it is the solution of the following optimization problem: Amin Ilb Eu: heme} {13) Consider a vector u E R",u 5% 0. Define the line 11'. := span(u). Find a matrix I"; {in terms of the vector n} such that for any vector x E R", the vector ['53: returns the orthogonal projection of 3: onto the line .6