For each of the following matrices A, find eigenvalues and eigenvectors (using Mathe- matica if you...

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For each of the following matrices A, find eigenvalues and eigenvectors (using Mathe- matica if you like) and draw clear phase plots for the system u' = Au, and classify the origin as an attractor, repellor, center, spiral attractor, or spiral repellor. Use a ruler (or electronic equivalent) for drawing axes. Draw arrows in the correct direction, and when eigenvectors are real, draw lines that clearly indicate the eigenspaces. 1. A = 2. A = 3. A = 4. A = -3 2 -2 2 2 0 -5 2 -20 20 [2 0-2 0 For each of the following matrices A, find eigenvalues and eigenvectors (using Mathe- matica if you like) and draw clear phase plots for the system u' = Au, and classify the origin as an attractor, repellor, center, spiral attractor, or spiral repellor. Use a ruler (or electronic equivalent) for drawing axes. Draw arrows in the correct direction, and when eigenvectors are real, draw lines that clearly indicate the eigenspaces. 1. A = 2. A = 3. A = 4. A = -3 2 -2 2 2 0 -5 2 -20 20 [2 0-2 0

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