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South Korea USCM
2018 Korea USCM
2
rank 1 projection
rank 1 projection
Source: 2018 South Korea USCM P2
August 14, 2020
linear algebra
rank
trace
matrix
college contests
Problem Statement
Suppose a
n
×
n
n\times n
n
×
n
real matrix
A
A
A
satisfies
tr
(
A
)
=
2018
\text{tr}(A)=2018
tr
(
A
)
=
2018
,
rank
(
A
)
=
1
\text{rank}(A)=1
rank
(
A
)
=
1
. Prove that
A
2
=
2018
A
A^2=2018 A
A
2
=
2018
A
.
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