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Greece National Olympiad
1987 Greece National Olympiad
2
determinant AB=0
determinant AB=0
Source: 1987 Greece MO Grade XII p2
September 6, 2024
linear algebra
matrix
determinant
Problem Statement
Let
A
=
(
α
i
j
)
A=(\alpha_{ij})
A
=
(
α
ij
)
be a
m
x
n
m\,x\,n
m
x
n
matric and
B
=
(
β
k
l
)
B=(\beta_{kl})
B
=
(
β
k
l
)
be a
n
x
m
n\,x\, m
n
x
m
matric with
m
>
n
m>n
m
>
n
. Prove that
D
(
A
⋅
B
)
=
0
D(A\cdot B)=0
D
(
A
⋅
B
)
=
0
.
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