Problem 6 for α 0 consider the system dx dt t 2 α 1

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Problem 6: For α 0, consider the system d~x dt ( t ) = 2 - α 1 3 ~x ( t ) . There exists c > 0 so that the phase portrait for this system has an unstable node if 0 α < c , and has an unstable spiral if α > c . Find this value for c . (a) c = 0 (b) c = 1 4 (c) c = 1 2 (c) c = 1 (c) c = 2
Test Section 2: Written Problems. Written Problem 1 [14pts]: Find the eigenvalues of the matrix A = 1 1 1 0 1 1 0 1 1 . For each eigenvalue, find an eigenvector.
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