Exam3A200 - M340L EXAM 3A 2:00 FALL, 2009 Dr. Schurle Your...

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M340L EXAM 3A 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 3 1 1 8 4 3 3 6 17 5 - 2 - 4 - 4 8 ? If so, find a basis for its eigenspace. If not, justify your answer.
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A = 1 0 27 2 5 - 8 3 0 1 . (b) Can you tell whether A is diagonalizable, yes or no? Justify your answer. 5. (10 points) The eigenvalues of the matrix A = 11 - 16 4 24 - 45 12 84 - 168 45 are λ = 3 , 3 , 5. Diagonalize
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This note was uploaded on 03/06/2010 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.

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Exam3A200 - M340L EXAM 3A 2:00 FALL, 2009 Dr. Schurle Your...

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