Solving Equations with [itex] ||x||_1=1[/tex]: Help Needed

[dirk_mec1]

Homework Statement

http://img205.imageshack.us/img205/3065/81913554uq8.png

Homework Equations

http://img236.imageshack.us/img236/7978/54438604he4.png

The Attempt at a Solution

I think it is crucial that [itex]||x||_1=1[/tex] but I don't see how I can use that info. Can someone help me?[/itex]

 

[Pere Callahan]

Try to show
$$||A||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$
and
$$||A||_1 \leq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$
separately. Can you prover either of these statements?

Hint: For the first one it is enough to find an x with norm one such that
$$||Ax||_1 \geq \max_{1\leq j\leq n}{\sum_{i=1}^n{|a_{ij}|}}$$