Consider the linear system -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3+i -3-i d1 = i , v1 = , and A2 = -i U2 = b. Find the real-valued solution to the initial value problem —Зул — 2у2, Y1(0) = -1, 5y1 + 3y2, Y2(0) = 5. %3D Use t as the independent variable in your answers. Y1(t) Y2(t)
Consider the linear system -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. -3+i -3-i d1 = i , v1 = , and A2 = -i U2 = b. Find the real-valued solution to the initial value problem —Зул — 2у2, Y1(0) = -1, 5y1 + 3y2, Y2(0) = 5. %3D Use t as the independent variable in your answers. Y1(t) Y2(t)
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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Question
Consider the linear system
y→′=[−3−253]y→.
- Find the eigenvalues and eigenvectors for the coefficient matrix.
λ1= , v→1= [ ] , and λ2= , v→2= [ ] - Find the real-valued solution to the initial value problem
{y1′=−3y1−2y2,y1(0)=−1,y2′=5y1+3y2,y2(0)=5.
Use t as the independent variable in your answers.
y1(t)=
y2(t)=

Transcribed Image Text:Consider the linear system
j' =
j.
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
-3+i
-3-i
A1 = i
v1 =
, and A, =
-i
v2 =
5
b. Find the real-valued solution to the initial value problem
— Зул — 2у2,
5y1 + 3y2,
ул (0) — —1,
Y2(0) = 5.
Use t as the independent variable in your answers.
Y1(t)
Y2(t)
||||
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