'"W\\\"'/ *_ mini:1,...,n[7'ii[ ' (f) Show that for any nonsingular A 6 (Cnxn, \"AX 1\" HXA 1\"} H A 2 max{ . ( ) IIXA Ill' IIAX Ill (Hz'nt: AX I = A(XA I)A-1.) 4. Let A E men and b E (Cm. We will discuss a variant of Ax m b where the error occurs only in A. Note that in ordinary least squares we assume that the error occurs only in b while in total least squares we assume that it occurs in both A and b. (a) Show that if 0 75 x E C", then >1: 2 2 xx Ax [Av-m.) F (b) Show that the matrix E = (b _ AX)X* E men x*x has the smallest 2norm among all E E (men that satisfy (A + E)x = b. (c) Let A, b, and x be given and xed. What are the solutions of min ||E||2 and min ||E||p (A+E)x=b (A+E)x=b where the minimum is taken over all E 6 men such that (A + E)x = b? STAT 309 ASSIGNMENT 2 (d) Given a E C\