1. The problem statement, all variables and given/known data Consider the vector space R^2, Decide whether or not the following are norms defined on R^2. If they are, verify all axioms of a norm, if not, demonstrate by counter example some axioms which fails. For x=(x_1,x_2) in R^2 2. Relevant equations (i) || ||_#: R^2 defined by ||x||_#=|x_1|+2|x_2| (ii) || ||_3:R^2 defined by ||x||=3|x_1| 3. The attempt at a solution How do I decide whether or not the above are norms on R^2?