MathDB
Problems
Contests
National and Regional Contests
Romania Contests
District Olympiad
2009 District Olympiad
1
Romania District Olympiad 2009 - Grade XI
Romania District Olympiad 2009 - Grade XI
Source:
April 10, 2011
algebra
polynomial
linear algebra
linear algebra unsolved
Problem Statement
Let
A
,
B
,
C
∈
M
3
(
R
)
A,B,C\in \mathcal{M}_3(\mathbb{R})
A
,
B
,
C
∈
M
3
(
R
)
such that
det
A
=
det
B
=
det
C
\det A=\det B=\det C
det
A
=
det
B
=
det
C
and
det
(
A
+
i
B
)
=
det
(
C
+
i
A
)
\det(A+iB)=\det(C+iA)
det
(
A
+
i
B
)
=
det
(
C
+
i
A
)
. Prove that
det
(
A
+
B
)
=
det
(
C
+
A
)
\det (A+B)=\det (C+A)
det
(
A
+
B
)
=
det
(
C
+
A
)
.
Back to Problems
View on AoPS