18. Constructing Matrix V Cont’d
When λ = 1
"
5 − λ 2
2 2 − λ
#
=
"
4 2
2 1
#
(18)
By row reduction form, we have:
"
2 1
4 2
#
=>
"
2 1
0 0
#
(19)
Forming equations with some variables:
2x + y = 0 (20)
Our eigenvector becomes: (1, −2)t
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19. Let Z be the egigenvectors of the various eigenvalues.
Z =
"
2 1
1 −2
#
We normalized each column of Z to get V
V =
"
2
√
5
5
√
5
5
√
5
5 −2
√
5
5
#
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20. Constructing U matrix
A = UΣV T
(21)
U = {u1, u2} (22)
u1 =
1
s1
Av1 (23)
u2 =
1
s2
Av2 (24)
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