Consider the linear system ● a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = -i Find the real-valued solution to the initial value problem yı(t) = y₂(t) = , V₁ = Use t as the independent variable in your answers. A 1 Jyí ly/₂ ÿ' = 9- and A₂ = i -3y1 - 2y2, 5y1 + 3y2, y1 (0) = 9, Y2 (0) = -10. v₂ = - 3/3 + 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the linear system
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
A₁ = -i
Find the real-valued solution to the initial value problem
Use t as the independent variable in your answers.
yı(t) =
y₂(t) =
V₁ =
1
3
5
i
5
[yí
ly ₂
= [ ³²
5
y' =
ÿ.
and A₂ = i
-3y1 - 2y2,
5y1 + 3y2,
y₁ (0) = 9,
Y2(0) = -10.
V₂
134
Transcribed Image Text:Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = -i Find the real-valued solution to the initial value problem Use t as the independent variable in your answers. yı(t) = y₂(t) = V₁ = 1 3 5 i 5 [yí ly ₂ = [ ³² 5 y' = ÿ. and A₂ = i -3y1 - 2y2, 5y1 + 3y2, y₁ (0) = 9, Y2(0) = -10. V₂ 134
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