Suppose Q = [91 92] is a 3 by 2 matrix with orthonormal columns.
(a) (3 pts) Write down the orthogonal projection matrix onto the column space of Q.
(b) (3 pts) Describe the null spaces of Q, Q^T and QQ^T .
(c) (4 pts) Suppose b = 2q₁ +3q2 +4q3, where q3 is orthogonal to both q₁ and q2. Find the least squares solution to Qx = b. What is the orthogonal projection of b onto the column space of Q?