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1
IMC 1996 Problem 1
IMC 1996 Problem 1
Source: IMC 1996
March 5, 2021
linear algebra
matrix
Problem Statement
Let
A
=
(
a
i
j
)
∈
M
(
n
+
1
)
×
(
n
+
1
)
(
R
)
A=(a_{ij})\in M_{(n+1)\times (n+1)}(\mathbb{R})
A
=
(
a
ij
)
∈
M
(
n
+
1
)
×
(
n
+
1
)
(
R
)
with
a
i
j
=
a
+
∣
i
−
j
∣
d
a_{ij}=a+|i-j|d
a
ij
=
a
+
∣
i
−
j
∣
d
, where
a
a
a
and
d
d
d
are fixed real numbers. Calculate
det
(
A
)
\det(A)
det
(
A
)
.
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