Problem 6: Consider a full rank m x n matrix A with m

Please solve as soon as possible

Extracted text: Problem 6: Consider a full rank m x n matrix A with m < n.="" a.="" show="" that="" the="" null-space="" n(a)="" is="" a="" convex="" set.="" is="" it="" true="" for="" every="" a?="" b.="" now,="" suppose="" we="" have="" been="" provided="" with="" a="" vector="" y="" €="" r".="" we="" want="" to="" find="" another="" vector="" x*="" which="" is="" closest="" (in="" terms="" of="" l2="" norm)="" to="" y="" such="" that="" x*="" €="" n(a).="" formulate="" the="" problem="" in="" terms="" of="" constrained="" optimization="" problem="" sing="" appropriate="" lagrangian,="" and="" solve="" it="" to="" find="" x*.="" you="" are="" not="" allowed="" to="" directly="" use="" right-pseudoinverse="" formulae="" here="" in="" any="">