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2011 CIIM
Problem 4
CIIM 2011 Problem 4
CIIM 2011 Problem 4
Source:
June 9, 2016
CIIM 2011
undergraduate
Problem Statement
For
n
≥
3
n \geq 3
n
≥
3
, let
(
b
0
,
b
1
,
.
.
.
,
b
n
−
1
)
=
(
1
,
1
,
1
,
0
,
.
.
.
,
0
)
.
(b_0, b_1,..., b_{n-1}) = (1, 1, 1, 0, ..., 0).
(
b
0
,
b
1
,
...
,
b
n
−
1
)
=
(
1
,
1
,
1
,
0
,
...
,
0
)
.
Let
C
n
=
(
c
i
,
j
)
C_n = (c_{i, j})
C
n
=
(
c
i
,
j
)
the
n
×
n
n \times n
n
×
n
matrix defined by
c
i
,
j
=
b
(
j
−
i
)
m
o
d
n
c_{i, j} = b _{(j -i) \mod n}
c
i
,
j
=
b
(
j
−
i
)
mod
n
. Show that
det
(
C
n
)
=
3
\det (C_n) = 3
det
(
C
n
)
=
3
if
n
n
n
is not a multiple of 3 and
det
(
C
n
)
=
0
\det (C_n) = 0
det
(
C
n
)
=
0
if
n
n
n
is a multiple of 3.
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