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Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x0 -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = { u: u = a¡u¡ + azu2, - 0 < a1, az < o} Describe the behavior of solutions as t → o if xo E S. uj = 0 Jand u2 = 0. uj = 1 and u2 = uj = o Jand uz = uj = 1 Jand u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector

Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x0 -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = { u: u = a¡u¡ + azu2, - 0 < a1, az < o} Describe the behavior of solutions as t → o if xo E S. uj = 0 Jand u2 = 0. uj = 1 and u2 = uj = o Jand uz = uj = 1 Jand u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Find constant 3x1 vectors u and u2 such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x. -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = {u: u = a¡u¡ + ażu2, - o < a1, az < ∞} Describe the behavior of solutions as t → oif xo £ S. uj = 0 Jand u2 = uj = 1 Jand u2 = uj = o Jand u2 = uj = 1 and u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector
Transcribed Image Text:Find constant 3x1 vectors u and u2 such that the solution of the initial value problem 2 -4 -3 x' = 3 -5 -3 x, x(0) = x. -2 2 1 tends to (0,0,0)" as t → o for any xo € S, where S = {u: u = a¡u¡ + ażu2, - o < a1, az < ∞} Describe the behavior of solutions as t → oif xo £ S. uj = 0 Jand u2 = uj = 1 Jand u2 = uj = o Jand u2 = uj = 1 and u2 = If xo ¢ S, then x(t) approaches as → o the line determined by the vector
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