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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
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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Consider the linear system

y→′=[−3−253]y→.

  1. Find the eigenvalues and eigenvectors for the coefficient matrix.
    λ1=   , v→1=
    [   ]
     
    		, and λ2=   , v→2=
    [   ]
     


  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)= 

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) ||||
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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