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1
Romania National Olympiad 2010 - Grade XI
Romania National Olympiad 2010 - Grade XI
Source:
April 10, 2011
linear algebra
matrix
linear algebra unsolved
Problem Statement
Let
a
,
b
∈
R
a,b\in \mathbb{R}
a
,
b
∈
R
such that
b
>
a
2
b>a^2
b
>
a
2
. Find all the matrices
A
∈
M
2
(
R
)
A\in \mathcal{M}_2(\mathbb{R})
A
∈
M
2
(
R
)
such that
det
(
A
2
−
2
a
A
+
b
I
2
)
=
0
\det(A^2-2aA+bI_2)=0
det
(
A
2
−
2
a
A
+
b
I
2
)
=
0
.
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