2130_Chapter7_Notes

E all entries are real numbers and a bi is a complex

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Unformatted text preview: v3 = −v1 − v2 c1 1 0 c2 = c1 0 + c2 1 =⇒ v = −c1 − c2 −1 −1 Label v(2) 1 = 0 −1 and (c1 or c2 nonzero) 0 v(3) = 1 . −1 10 / 11 Exa 2 (slide 4) 1 1 (1) = 1 = (1) = 1 e2t λ1 = 2, v ⇒x 1 1 1 0 λ2 = −1, v(2) = 0 , v(3) = 1 −1 −1 0 1 =⇒ x(2) = 0 e−t , x(3) = 1 e−t −1 −1 General solution: 1 1 0 x = c1 1 e2t + c2 0 e−t + c3 1 e−t . 1 −1 −1 6 11 / 11 APMA 2130 Section 7.6: Complex Eigenvalues Post-Lecture Handout Dr. Bernard Fulgham University of Virginia July 22, 2013 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 How to Solve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Solution (slide 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4...
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