Exercise 4 ( 10 points ) . The two parts in this exercise are independent . 1 . ( 5 points ) Let ( E, \\\\. (1) be a normed space and let a = [a] . .... and be a family of ~ real numbers . Define 11 . 11 : Ex -> IR by n. /zella = > aillwill for all u = ( 21 , ... , Un ) E En . 2 = 1 Find a necessary and sufficient condition on the family a for ( Ex , | | ull, ) to be a normed space . 2 . Define 11 . 11 : Re~x~ ~ R by 1/All = ~ max\\ ` , JE ( 1 . .... 12 ] laijl for all A = ( ajj) ; E RRxn. ( a ) ( 2 points ) Show that ( RR~xn, 1 . 1 1) is a normed space . ( b ) ( 3 points) Show that I| ABI!