[Solved] MATH307 Individual Homework9

Instructions: Read textbook pages 46 to 51 before working on the homework problems. Show all steps to get full credits.

1. Write down the default inner product in C³ and show that the induced norm corresponding to this default inner product is actually the 2-norm. Let

1+ i 1 u = 2i ,v = 3 i ,

3+ i i

find the norm of u and the distance between u,v under the default inner product in C³.

2. Find the 1,2, norm unit balls in R² and sketch them. Find all the x R² that satisfies kxk₁ =kxk₂ =kxk=1.