# Exam3B200 - M340L EXAM 3B 2:00 FALL, 2009 Dr. Schurle Your...

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M340L EXAM 3B 2:00 FALL, 2009 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (10 points) Explain in detail why eigenvalues of a matrix A must be solutions of det( A - λI ) = 0.

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YOUR SCORE: /100 2. (10 points) Explain in detail why a p × p matrix A is diagonalizable exactly when there is a basis for R p consisting of eigenvectors of A . 3. (10 points) Is 6 an eigenvalue of the matrix 7 2 1 1 2 10 2 4 1 4 7 10 1 4 0 24 ? If so, ﬁnd a basis for its eigenspace. If not, justify your answer.
4. (10 points) (a) Find the eigenvalues of the matrix A = 5 8 2 0 6 0 32 - 2 5 . (b) Can you tell whether A is diagonalizable, yes or no? Justify your answer. 5. (10 points) The eigenvalues of the matrix A = 0 - 2 2 - 5 - 3 5 - 8 - 8 10 are λ = 2 , 2 , 3. Diag- onalize A if possible and if not, explain why not.

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## Exam3B200 - M340L EXAM 3B 2:00 FALL, 2009 Dr. Schurle Your...

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