Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = , 71 = b. Find the real-valued solution to the initial value problem [y{ (Y/₂2 -3 -2] ✓-89 ÿ' = 5 3 Use t as the independent variable in your answers. = = ÿ. and X₂ -3y₁ - 2y2, 5y1 + 3y2, = 1, V₂ = y₁ (0) = -5, 3₂ (0) = 10.
Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ = , 71 = b. Find the real-valued solution to the initial value problem [y{ (Y/₂2 -3 -2] ✓-89 ÿ' = 5 3 Use t as the independent variable in your answers. = = ÿ. and X₂ -3y₁ - 2y2, 5y1 + 3y2, = 1, V₂ = y₁ (0) = -5, 3₂ (0) = 10.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the linear system
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
A₁ = -i
,7₁ =
b. Find the real-valued solution to the initial value problem
[y{
ly/₂2
-3
*'-[-D
y' =
5
3
Use t as the independent variable in your answers.
y₁ (t) =
y2 (t) =
=
=
, and A₂ =
-3y₁ - 2y2,
5y₁ + 3y2,
, 7₂ =
y₁ (0) = -5,
Y2(0) = 10.
18
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