Prove that the following formulas define norms on R2:
(a) ||v|| = √221 + 3v22
(b) ||v|| = √2v21] - v1v2 + 2v22
(c) ||v|| =2|v1| + |v2|
(d) ||v|| = max{ 2|v1|, |v2| }
(e) ||v|| = max{ |v1, - v2|, |v1 + v2|}
(f) ||v|| = |v1, - v2| + v1, + v2|