final exam fall 2007 - Engineering Mathematics(E35 317...

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Engineering Mathematics (E35 317) Final Exam December 18, 2007 This exam contains 18 multiple-choice problems worth two points each, five short-answer problems worth one point each, and nine true-false problems worth one point each, for an exam total of 50 points. Part I. Multiple-Choice Clearly circle the only correct response. Each is worth two points. 1. Find the solution of the following initial value problem. C  *C œ Ð>  #Ñ CÐ!Ñ œ ' C Ð!Ñ œ ! ww w $ (A) CÐ>Ñ œ # $>  $> / cos sin " $ #> (B) CÐ>Ñ œ # $>  $> / cos sin #> (C) CÐ>Ñ œ # $>  $Ð>  #Ñ?Ð>  #Ñ cos sin " $ (D) CÐ>Ñ œ # $>  $Ð>  #Ñ?Ð>  #Ñ cos sin (E) CÐ>Ñ œ ' $>  $> / cos sin " $ #> (F) CÐ>Ñ œ ' $>  $> / cos sin #> (G) CÐ>Ñ œ ' $>  $Ð>  #Ñ?Ð>  #Ñ cos sin " $ (H) CÐ>Ñ œ ' $>  $Ð>  #Ñ?Ð>  #Ñ cos sin 2. Find . _ " # Ð Ð=  %ÑÑ ln (A) #> " #> cos (B) #> " > cos (C) #> # > cos (D) #> > # cos (E) > #> cos (F) #> #> cos (G) #> " #> sin (H) #> " > sin (I) #> # > sin (J) #> > # sin (K) > #> sin (L) #> #> sin
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3. Find the dimension of the null space of the following matrix. Ô × Õ Ø # " " # ! ! ( " ' # " $ " # " (A) ! (B) " (C) # (D) $ (E) % (F) & 4. Consider the matrix A œ " " " " " " " " " " " " " " " " Ô × Ö Ù Ö Ù Õ Ø . Which of the following vectors are eigenvectors of A ? (I) (II) (III) Ô × Ô × Ô × Ö Ù Ö Ù Ö Ù Ö Ù Ö Ù Ö Ù Õ Ø Õ Ø Õ Ø " " ! " ! ! " ! ! " " !
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