Home > Olympiad > IMC 2012 Problem 2

IMC 2012 Problem 2

Let ${n}$ be a fixed positive integer. Determine the smallest positive rank of an ${n \times n}$ matrix that has zeros along the main diagonal and strictly positive real numbers off the main diagonal.

Advertisements
Categories: Olympiad Tags: ,
1. August 1, 2012 at 4:03 pm

Hello,

This is one of problems that interests me. Have you the answer and can you share it please. Many thanks 🙂

• August 2, 2012 at 11:36 am

It is easy to see that if $n \geq 3$ then the rank of the matrix is at least $3$. The main difficulty is to find an example of a matrix with rank exactly $3$.

1. No trackbacks yet.