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Vojtěch Jarník IMC
2013 VJIMC
Problem 2
matrix, a_(ij)=b_(ij)+1
matrix, a_(ij)=b_(ij)+1
Source: VJIMC 2013 1.2
May 30, 2021
linear algebra
matrix
Problem Statement
Let
A
=
(
a
i
j
)
A=(a_{ij})
A
=
(
a
ij
)
and
B
=
(
b
i
j
)
B=(b_{ij})
B
=
(
b
ij
)
be two real
10
×
10
10\times10
10
×
10
matrices such that
a
i
j
=
b
i
j
+
1
a_{ij}=b_{ij}+1
a
ij
=
b
ij
+
1
for all
i
,
j
i,j
i
,
j
and
A
3
=
0
A^3=0
A
3
=
0
. Prove that
det
B
=
0
\det B=0
det
B
=
0
.
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