The following system has two distinct real eigenvalues, but one eigenvalue is equal to
Chapter 11, Problem 67(choose chapter or problem)
The following system has two distinct real eigenvalues, but one eigenvalue is equal to 0: dx dt = _ 4 8 1 2 _ x(t) (11.36) (a) Find both eigenvalues and the associated eigenvectors. (b) Use the general solution (11.26) to find x1(t) and x2(t). (c) The direction field is shown in Figure 11.31. Sketch the lines corresponding to the eigenvectors. Compute dx2/dx1, and conclude that all direction vectors are parallel to the line in the direction of the eigenvector corresponding to the nonzero eigenvalue. Describe in words how solutions starting at different points behave.
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