Let A e Rmxn, m > n, rank(A) = n, and beR. The least squares problem min || Acc 6|| (*) can be formulated as the linear algebraic system Im AT 1] [2] = (**) where Im stands for the m x m identity matrix and r = b - Ar ER" is the residual. (a) Using the normal equations, show that the component z of the solution of (**) solves the least squares problem (*). (b) (Extra Credits) Given a decomposition of A according to R A = Q 0 with an orthogonal matrix Q ERmxm and a regular upper triangular matrix ReRnxn, show that by orthogonal row and column transformations the linear system Im A AT 0 4] "=1 can be transformed to the form In 0 RT 0 R Im-n 0 0 0 Specify the relation between the vectors h, d, fi, and f, p. Let A e Rmxn, m > n, rank(A) = n, and beR. The least squares problem min || Acc 6|| (*) can be formulated as the linear algebraic system Im AT 1] [2] = (**) where Im stands for the m x m identity matrix and r = b - Ar ER" is the residual. (a) Using the normal equations, show that the component z of the solution of (**) solves the least squares problem (*). (b) (Extra Credits) Given a decomposition of A according to R A = Q 0 with an orthogonal matrix Q ERmxm and a regular upper triangular matrix ReRnxn, show that by orthogonal row and column transformations the linear system Im A AT 0 4] "=1 can be transformed to the form In 0 RT 0 R Im-n 0 0 0 Specify the relation between the vectors h, d, fi, and f, p