find a norm on R2 for which||(0,1)||=1=||(1,0)|| but ||(1,1)||=0.000001

hints: ||(a,b)|| = A |a+b|+B|a-b|

by the hints i have A+B=1 and

2A=0.000001

then solved the equations system i get A=0.0000005

B=1-A=0.9999995 then ||(a,b)|| = 0.000001|a+b|+0.9999995 |a-b|

is it the

answers???