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1
Linear algebra impossibility
Linear algebra impossibility
Source:
December 16, 2019
Cayley-Hamilton
linear algebra
Problem Statement
Do exist pairwise distinct matrices
A
,
B
,
C
∈
M
2
(
R
)
A,B,C\in \mathcal{M}_2(\mathbb{R})
A
,
B
,
C
∈
M
2
(
R
)
verifying the following properties?
(i)
det
A
=
det
C
\text{(i)} \det A=\det C
(i)
det
A
=
det
C
(ii)
A
B
=
C
,
B
C
=
A
,
C
A
=
B
\text{(ii)} AB=C,BC=A,CA=B
(ii)
A
B
=
C
,
BC
=
A
,
C
A
=
B
(iii)tr
A
,
tr
B
≠
0
\text{(iii)} \text{tr} A,\text{tr} B\neq 0
(iii)
tr
A
,
tr
B
=
0
Robert Pop
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