please send handwritten solution for Q 3.21 part a Only Handwritten solution accepted 3.21 Pointuwise maximum and supremum. Show that the following functions f : R" → R areconvex.(a) f(x):= max;=1,.,k ||Aª)x – b@)||, where A) e Rmxn, b(i) e R™ and || · || is a normon R™.(b) ƒ(x) = E, a|g on R", where |æ| denotes the vector with |x|; = |xi| (i.e., |x| isthe absolute value of x, componentwise), and |x|f2] is the ith largest component of|x|. In other words, |æ|1], |x|(2), ..., |æ|[n] are the absolute values of the componentsof x, sorted in nonincreasing order.

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3.21 Pointwise maximum and supremum. Show that the following functions f: R" → R are convex. (a) f(x) = maxi=1,...,k ||A®x – b(@) ||, where A e R™×", b(^) e R" and || - || is a norm on Rm. (b) f(x) = EE r|g on R", where |x| denotes the vector with |r|i = |xi| (i.e., |x| is the absolute value of x, componentwise), and |æ|1] is the ith largest component of |x|. In other words, |æ|1], |x||2), ..., |x|[n] are the absolute values of the components of x, sorted in nonincreasing order.