For 1), you have to find a for any such that if .
Hint : How do you calculate ?
As a sidenote... : you're currently working on
Since we're in finite dimension, all the norms are equivalent.
So you can choose whatever norm you want :
norm 1 :
norm 2 :
and by noting (a,b)-(c,d)=(a-c,b-d)
maybe the norm 1 would be easier to manipulate