Exercise 3. Let ||- || be a vector norm on R. A vector norm ||- ||....

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Exercise 3. Let ||- || be a vector norm on R". A vector norm ||- ||. on R" defined as |zx| x40x is called the dual norm of ||- ||- (a) 8 pts. Prove that (1) defines a norm. (b) 5 pts. Show that for all x, y eR" we have ||z| = max |xy|≤|xy|.. (c) 8 pts. Show that on R" the 1-norm ||- ||₁ is dual to the co-norm || || and vice versa. Exercise 3. Let ||- || be a vector norm on R". A vector norm ||- ||. on R" defined as |zx| x40x is called the dual norm of ||- ||- (a) 8 pts. Prove that (1) defines a norm. (b) 5 pts. Show that for all x, y eR" we have ||z| = max |xy|≤|xy|.. (c) 8 pts. Show that on R" the 1-norm ||- ||₁ is dual to the co-norm || || and vice versa.

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ANSWER a To prove that 1 defines a norm we need to show that it satisfies the following properties z ... View the full answer