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The general solution of the linear system X' = AX is given. A = = (³ -2). x(t) = c₁ c₁(1) et. et + c₂ e-t 3 3 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O All solutions become unbounded and y = 3x serves as the asymptote. O All solutions become unbounded and y = x serves as the asymptote. If X(0) = X lies on the line y = x, then x(t) approaches (0, 0) along this line. Otherwise X(t) becomes unbounded and y = 3x serves as an asymptote. If X(0) = X lies on the line y = 3x, then x(t) approaches (0, 0) along this line. Otherwise x(t) becomes unbounded and y = x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). 2 1 (1, 1) x -2 -1 1 2 4 -2 2 1 (1, 1) 4 2 -2 (1, 1) 2 x 4 -4 i 2 (1, 1) 1 x 1 2 2 1 1 2 x

The general solution of the linear system X' = AX is given. A = = (³ -2). x(t) = c₁ c₁(1) et. et + c₂ e-t 3 3 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O All solutions become unbounded and y = 3x serves as the asymptote. O All solutions become unbounded and y = x serves as the asymptote. If X(0) = X lies on the line y = x, then x(t) approaches (0, 0) along this line. Otherwise X(t) becomes unbounded and y = 3x serves as an asymptote. If X(0) = X lies on the line y = 3x, then x(t) approaches (0, 0) along this line. Otherwise x(t) becomes unbounded and y = x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). 2 1 (1, 1) x -2 -1 1 2 4 -2 2 1 (1, 1) 4 2 -2 (1, 1) 2 x 4 -4 i 2 (1, 1) 1 x 1 2 2 1 1 2 x

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 71E: Find a system of two equations in two variables, x1 and x2, that has the solution set given by the...
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The general solution of the linear system X' = AX is given. A = = (³ -2). x(t) = c₁ c₁(1) et. et + c₂ e-t 3 3 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O All solutions become unbounded and y = 3x serves as the asymptote. O All solutions become unbounded and y = x serves as the asymptote. If X(0) = X lies on the line y = x, then x(t) approaches (0, 0) along this line. Otherwise X(t) becomes unbounded and y = 3x serves as an asymptote. If X(0) = X lies on the line y = 3x, then x(t) approaches (0, 0) along this line. Otherwise x(t) becomes unbounded and y = x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). 2 1 (1, 1) x -2 -1 1 2 4 -2 2 1 (1, 1) 4 2 -2 (1, 1) 2 x 4 -4 i 2 (1, 1) 1 x 1 2 2 1 1 2 x
Transcribed Image Text:The general solution of the linear system X' = AX is given. A = = (³ -2). x(t) = c₁ c₁(1) et. et + c₂ e-t 3 3 (a) In this case discuss the nature of the solution in a neighborhood of (0, 0). O All solutions become unbounded and y = 3x serves as the asymptote. O All solutions become unbounded and y = x serves as the asymptote. If X(0) = X lies on the line y = x, then x(t) approaches (0, 0) along this line. Otherwise X(t) becomes unbounded and y = 3x serves as an asymptote. If X(0) = X lies on the line y = 3x, then x(t) approaches (0, 0) along this line. Otherwise x(t) becomes unbounded and y = x serves as an asymptote. O All solutions spiral toward (0, 0). (b) With the aid of a calculator or a CAS, graph the solution that satisfies X(0) = (1, 1). 2 1 (1, 1) x -2 -1 1 2 4 -2 2 1 (1, 1) 4 2 -2 (1, 1) 2 x 4 -4 i 2 (1, 1) 1 x 1 2 2 1 1 2 x
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