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2022 CIIM
2
2
Part of
2022 CIIM
Problems
(1)
Linear Algebra CIIM 2022
Source: http://ciim.uan.edu.co/ciim-2022
3/31/2023
Let
v
∈
R
2
v \in \mathbb{R}^2
v
∈
R
2
a vector of length 1 and
A
A
A
a
2
×
2
2 \times 2
2
×
2
matrix with real entries such that: (i) The vectors
A
v
,
A
2
v
A v, A^2 v
A
v
,
A
2
v
y
A
3
v
A^3 v
A
3
v
are also of length 1. (ii) The vector
A
2
v
A^2 v
A
2
v
isn't equal to
±
v
\pm v
±
v
nor to
±
A
v
\pm A v
±
A
v
. Prove that
A
t
A
=
I
2
A^t A=I_2
A
t
A
=
I
2
.
linear algebra
vector
matrix