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Unformatted text preview: Mathematics 38 Differential Equations Examination 1 February 18, 2010 No calculators, notes, or books are allowed. Please make sure all electronic devices are turned off and out of sight. Show all work and cross out work you do not want graded! Remember to sign your blue book. With your signature you are pledging that you have neither given nor received assistance on this exam. Good luck! Please put the answers to problems 1–10 on the blue book cover in the corresponding box, as shown here: 1. (5 points, answer only, no partial credit) Can the system below be solved by Cramer’s rule? x +2 y + z = 0 3 x +6 y +3 z = 0 x + z = 0 Solution: No, the second equation is 3 times the first, so the determinant of the coefficient matrix is zero. 2. (5 points, answer only, no partial credit) Consider the following system of equations: x +2 y + z = 0 2 x y +3 z = 0 2 x 6 y +4 z = 0 Choose one answer: The system has a. a unique solution, b. no solution, c. more than 1 solution. d. None of the above. Solution: c. : d. is clearly impossible, a. is impossible because Cramer’s test gives a zero determinant, and b. is not true because x = y = z = 0 is an obvious solution. 3. (5 points, answer only, no partial credit) Choose one answer. det t 1 sin t ln t 1 t 4 cos t e t 3 tan t t √ t t 2 9 1 = a. 4 t 3 tan t , b. t sin t ln t , c. 3 t 3 tan t 3 t 2 , d. None of the above. Solution: d. ; subtract row 1 from row 2 first to make the matrix triangular; the determinant is 3 t 3 tan t ....
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This note was uploaded on 10/29/2010 for the course MATH MATH38 taught by Professor Hasselblatt during the Fall '10 term at Tufts.
 Fall '10
 Hasselblatt
 Differential Equations, Equations

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