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.

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


    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.

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