Question: 3. Given the matrix S= = [ = 11 36 -3 -10 6] a) Compute for its eigenvalues and their corresponding eigenvectors. (Select eigenvectors

3. Given the matrix S= = [ = 11 36 -3 -10

3. Given the matrix S= = [ = 11 36 -3 -10 6] a) Compute for its eigenvalues and their corresponding eigenvectors. (Select eigenvectors with the smallest possible whole number entries). [6pts] b) Let A be the eigenvalue matrix and R, the corresponding eigenvector matrix, compute for R- [2pts] c) Use the fact that S3 = RAR-1 to compute for S. [3pts] d) Solve the autonomous linear system du dt Su with initial value = u(0) = [ - ] [4pts]

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