We wish to solve the system 21 [sin(t) 1 [-²/3 via eigenvector decomposition. x' = V2 = 15 Let 71 be an eigenvector for the smaller eigenvalue of the coefficient matrix and 2 be an eigenvector for the larger eigenvalue. Let us pick the eigenvectors such that 7₁ [2] V2 = -3 6 = x + [13]. What are these eigenvectors: and

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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We wish to solve the system
21
x +
[sin(t)
X
1
via eigenvector decomposition.
-
Let 7₁ be an eigenvector for the smaller eigenvalue of the coefficient matrix and 72 be an
[]
√2
eigenvector for the larger eigenvalue. Let us pick the eigenvectors such that 1
=
7₁
V2
=
=
"
=
[²].
What are these eigenvectors:
Then fill in the equation to write it in the eigenvector decomposed form.
01&₁ + √2§₂
v1&1 +
√2§2 + V1
=
and
+02
Transcribed Image Text:We wish to solve the system 21 x + [sin(t) X 1 via eigenvector decomposition. - Let 7₁ be an eigenvector for the smaller eigenvalue of the coefficient matrix and 72 be an [] √2 eigenvector for the larger eigenvalue. Let us pick the eigenvectors such that 1 = 7₁ V2 = = " = [²]. What are these eigenvectors: Then fill in the equation to write it in the eigenvector decomposed form. 01&₁ + √2§₂ v1&1 + √2§2 + V1 = and +02
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