Least squares and qr factorization. suppose a is an m n matrix with linearly independent columns and qr factorization a = qr, and b is an m-vector. the vector a^x is the linear combination of the columns of a that is closest to the vector b, i. e., it is the projection of b onto the set of linear combinations of the columns of a. (a) show that a^x = qqt b. (the matrix qqt is called the projection matrix.) (b) show that = bk2. (this is the square of the distance between b and the closest linear combination of the columns of a.)