MathDB

Putnam 1999 B5

Source:

December 22, 2012

Putnamlinear algebramatrixvectortrigonometrycollege contests

Problem Statement

For an integer

n\geq 3

, let

\theta=2\pi/n

. Evaluate the determinant of the

n\times n

matrix

I+A

, where

I

is the

n\times n

identity matrix and

A=(a_{jk})

has entries

a_{jk}=\cos(j\theta+k\theta)

for all

j,k