A is an m×n matrix and b is in IRm. Mark each statement as True or False and justify each answer with one sentence or a sketch.

(a) The general least-squares problem is to ?nd a vector, x, that makes Ax as close as possible to b.
(b) If b is in the column space of A, then every solution of Ax = b is a least squares solution.

(c) A least-squares solution of Ax = b is a vector b x that satis?es Ab x = b b, where b b is the orthogonal projection of b onto ColA. (d) If the columns of A are linearly independent, then the equation Ax = b has exactly one least-squares solution.