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2001 District Olympiad
1
Romania District Olympiad 2001 - Grade XI
Romania District Olympiad 2001 - Grade XI
Source:
March 16, 2011
linear algebra
matrix
algebra
polynomial
linear algebra unsolved
Problem Statement
Let
A
∈
M
2
(
R
)
A\in \mathcal{M}_2(\mathbb{R})
A
∈
M
2
(
R
)
such that
det
(
A
)
=
d
≠
0
\det(A)=d\neq 0
det
(
A
)
=
d
=
0
and
det
(
A
+
d
A
∗
)
=
0
\det(A+dA^*)=0
det
(
A
+
d
A
∗
)
=
0
. Prove that
det
(
A
−
d
A
∗
)
=
4
\det(A-dA^*)=4
det
(
A
−
d
A
∗
)
=
4
.Daniel Jinga
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