Matrix L1-Norm: Max of Column Sums Explained

[gucci1]

Hi, for a homework problem I was asked to show that for an m x n matrix A, the l1-norm of the matrix is the max of the sums of the columns. What I tried to do was plug into the definition of the vector l1-norm with Ax for some x st the l1-norm of x is 1. This shows, after a bit of simplifying, the l1-norm of A is equal to the sum of the row sums of A. This is not at all what I was supposed to show, so does anyone know where I made a mistake? Thanks for any help!

 

[Fernando Revilla]

so does anyone know where I made a mistake? Thanks for any help!

Better if you show your work. At any case, have a look here.