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2018 IMC
3
3
Part of
2018 IMC
Problems
(1)
IMC 2018 P3
Source: IMC 2018 P3
7/24/2018
Determine all rational numbers
a
a
a
for which the matrix
(
a
−
a
−
1
0
a
−
a
0
−
1
1
0
a
−
a
0
1
a
−
a
)
\begin{pmatrix} a & -a & -1 & 0 \\ a & -a & 0 & -1 \\ 1 & 0 & a & -a\\ 0 & 1 & a & -a \end{pmatrix}
a
a
1
0
−
a
−
a
0
1
−
1
0
a
a
0
−
1
−
a
−
a
is the square of a matrix with all rational entries.Proposed by Daniël Kroes, University of California, San Diego
linear algebra
imc2018