Exam3B900

# Exam3B900 - M340L EXAM 3B 9:00 FALL, 2009 Dr. Schurle Your...

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M340L EXAM 3B 9:00 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 two vectors u and v in R p are orthogonal exactly when || u + v || 2 = || u || 2 + || v || 2 .

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YOUR SCORE: /100 2. (10 points) Using only algebra and deﬁnitions, show why eigenvectors v 1 and v 2 cor- responding to eigenvalues 3 and 5, respectively, for some matrix A must be linearly independent. 3. (10 points) Is 4 an eigenvalue of the matrix 5 2 1 1 2 8 2 4 1 4 5 10 1 4 0 22 ? 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 2 8 0 3 0 2 - 1 5 . (b) Can you tell whether A is diagonalizable, yes or no? Justify your answer. 5. (10 points) The eigenvalues of the matrix

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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.

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Exam3B900 - M340L EXAM 3B 9:00 FALL, 2009 Dr. Schurle Your...

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