Least squares with orthonormal columns. Suppose the mn matrix Q has orthonormal columns and b is an m -vector. Show that x^ = QTb is the vector that minimizes Qxb2 in two ways:

(a) Apply the pseudoinverse formula.

(b) Use the orthogonality condition that the least square solution must satisfy. Interpret your answer geometrically by drawing a picture for the case when m=3andn=2.