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Problems
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Undergraduate contests
IMC
2021 IMC
1
1
Part of
2021 IMC
Problems
(1)
IMC 2021, first day, problem 1
Source: IMC day1 , p1
8/4/2021
Let
A
A
A
be a real
n
×
n
n\times n
n
×
n
matrix such that
A
3
=
0
A^3=0
A
3
=
0
a) prove that there is unique real
n
×
n
n\times n
n
×
n
matrix
X
X
X
that satisfied the equation
X
+
A
X
+
X
A
2
=
A
X+AX+XA^2=A
X
+
A
X
+
X
A
2
=
A
b) Express
X
X
X
in terms of
A
A
A
linear algebra
IMC 2021