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IMC
2002 IMC
7
7
Part of
2002 IMC
Problems
(1)
IMC 2002 Problem 7
Source: IMC 2002
3/7/2021
Compute the determinant of the
n
×
n
n\times n
n
×
n
matrix
A
=
(
a
i
j
)
i
j
A=(a_{ij})_{ij}
A
=
(
a
ij
)
ij
,
a
i
j
=
{
(
−
1
)
∣
i
−
j
∣
if
i
≠
j
,
2
if
i
=
j
.
a_{ij}=\begin{cases} (-1)^{|i-j|} & \text{if}\, i\ne j,\\ 2 & \text{if}\, i= j. \end{cases}
a
ij
=
{
(
−
1
)
∣
i
−
j
∣
2
if
i
=
j
,
if
i
=
j
.
linear algebra
matrix