Fall 07 Exam 2

# Fall 07 Exam 2 - Engineering Mathematics(E35 317 Exam 2...

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Engineering Mathematics (E35 317) Exam 2 October 10, 2007 This exam contains seven multiple-choice problems worth two points each, eight true-false problems worth one point each, and four free-response problems worth 18 points altogether, for an exam total of 40 points. Part I. Multiple-Choice Clearly circle the only correct response. Each is worth two points. 1. Find the nullity of the matrix . Ô× ÕØ "#\$% & ' !!!! ! ! #%')" !" # (A) ! (B) " (C) # (D) \$ (E) % (F) & (G) ' 2. Find the eigenvalues of the matrix . ”• " " &\$ What is the larger eigenvalue? (A) # (B) " (C) ! (D) " (E) # (F) \$ (G) % (H) & (I) The eigenvalues are repeated, so there is no “larger” eigenvalue. (J) There are no real eigenvalues.

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3. The vector is an eigenvector for the matrix below. To what eigenvalue does it correspond? Ô× ÖÙ ÕØ " ! " ! " &* " \$ \$ % ' " !(# & " ) # " "" "" "& " ! %* "& ) "# " ( (A) % (B) \$ (C) # (D) " (E) ! (F) " (G) # (H) \$ (I) % 4. If the vector u has magnitude and the vector v has magnitude , and if u and v point in pp p p #\$ opposite directions, then what are the values of u • v and u v respectively?
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## This note was uploaded on 10/12/2008 for the course ESE 317 taught by Professor Hastings during the Spring '08 term at Washington University in St. Louis.

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Fall 07 Exam 2 - Engineering Mathematics(E35 317 Exam 2...

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