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Romania National Olympiad
2010 Romania National Olympiad
2
Romania National Olympiad 2010 - Grade XI
Romania National Olympiad 2010 - Grade XI
Source:
April 10, 2011
linear algebra
linear algebra unsolved
Problem Statement
Let
A
,
B
,
C
∈
M
n
(
R
)
A,B,C\in \mathcal{M}_n(\mathbb{R})
A
,
B
,
C
∈
M
n
(
R
)
such that
A
B
C
=
O
n
ABC=O_n
A
BC
=
O
n
and
rank
B
=
1
\text{rank}\ B=1
rank
B
=
1
. Prove that
A
B
=
O
n
AB=O_n
A
B
=
O
n
or
B
C
=
O
n
BC=O_n
BC
=
O
n
.
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