Question
Find the general solution for each of the given system of equations. Draw a phase portrait. Describe the behavior of the solutions as t rightarrow infinite. x' = [ ]x x' = [ ]x x' = [ ]x x' = [ ]x In each of the next four problems, the eigenvalues and eigenvectors of a matrix A are given. Consider the corresponding system x' = Ax. Without using a computer, draw each of the following graphs. Sketch a phase portrait of the system. Sketch the solution curve passing through the initial point (2,3). For the curve in part (ii), sketch the component plots of x1 versus t and x2 versus t on the same set of axes. lambda1 = -1, v1 = [-1 2]; lambda2 = -4, v2 = [1 2]. lambda1 = 1, v1 = [-1 2]; lambda2 = -4, v2 = [1 2]. lambda1 = -1, v1 = [-1 2]; lambda2 = 4, v2 = [1 2]. lambda1 = 1, v1 = [1 2]; lambda2 = 4, v2 = [1 -2]. In each of the next four problems, the eigenvalues and eigenvectors of a matrix A are given. Consider the corresponding system x' = Ax. Without using a computer, draw each of the following graphs. Sketch a phase portrait of the system. Sketch the trajectory passing through the initial point (2,3). lambda1 = -4, v1 = [-1 2]; lambda2 = -1, v2 = [1 2]. lambda1 = 4, v1 = [-1 2]; lambda2 = -1, v2 = [1 2]. lambda1 = -4, v1 = [-1 2]; lambda2 = 1, v2 = [1 2]. lambda1 = 4, v1 = [1 2]; lambda2 = 1, v2 = [1 -2]. Find the general solution for each of the given systems in terms of real-valued functions, and draw a phase portrait. Describe the behavior of the solutions as t rightarrow infinity. x' = [ ]x x' = [ ]x x' = [ ]x
Explanation / Answer
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