MathDB

Problem 4

Part of 2011 CIIM

Problems(1)

CIIM 2011 Problem 4

Source:

6/9/2016
For n≥3n \geq 3, let (b0,b1,...,bn−1)=(1,1,1,0,...,0).(b_0, b_1,..., b_{n-1}) = (1, 1, 1, 0, ..., 0). Let Cn=(ci,j)C_n = (c_{i, j}) the n×nn \times n matrix defined by ci,j=b(j−i)mod  nc_{i, j} = b _{(j -i) \mod n}. Show that det⁡(Cn)=3\det (C_n) = 3 if nn is not a multiple of 3 and det⁡(Cn)=0\det (C_n) = 0 if nn is a multiple of 3.
CIIM 2011undergraduate