2132worksheet4

2132worksheet4 - , 2 t ] (b) u 1 ( t ) = [2-t,t,-2], u 2 (...

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Polytechnic Institute of NYU MA 2132 Worksheet 4 Date: Print Name: Signature: ID #: Instructor: Jacobovits Problem Possible Points 1 16 2 30 3 30 4 12 5 12 Total 100
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Your signature: (1) Rewrite the differential equation as a first order system. (a) x 00 - tx 0 + x 2 = sin t (b) x 000 - x 00 + x = e t
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Your signature: (2) Find the matrix A and vector b if the given system is written as x 0 = Ax + b . (a) x 0 1 = - 2 x 1 + x 2 + cos(2 t ) x 0 2 = - x 1 - x 2 - 2sin(2 t ) (b) x 0 1 = e t x 1 - e - t x 2 x 0 2 = 2 e - t x 1 + 3 e t x 2 (c) x 0 1 = 2 x 1 + x 2 - x 3 + 2 e - t x 0 2 = x 1 - x 2 - e - t x 0 3 = x 1 + e t x 2
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Your signature: (3) Determine whether or not the given set of vector functions is linearly dependent. The in- terval of definition is assumed to be the set of all real numbers. (a) u 1 ( t ) = [2 t - 1 , - t ] and u 2 ( t ) = [ - t + 1
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Unformatted text preview: , 2 t ] (b) u 1 ( t ) = [2-t,t,-2], u 2 ( t ) = [ t,-1 , 2] and u 3 ( t ) = [2 + t,t-2 , 2] (c) u 1 ( t ) = [ e t , , 0], u 2 ( t ) = [0 , cos t, cos t ] and u 3 ( t ) = [0 , sin t, sin t ] Your signature: (4) Find the solution of the equation x = Ax , where A is the given matrix. A = ± 2 4-2-2 ¶ and x (0) = [1 , 3] Your signature: (5) Find the solution of the equation x = Ax , where A is the given matrix. A = 5 4-4-2-2 12 6 and x (0) = [-1 , 2 ,-8]...
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This note was uploaded on 03/21/2010 for the course MA 2132 taught by Professor King during the Spring '07 term at NYU Poly.

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2132worksheet4 - , 2 t ] (b) u 1 ( t ) = [2-t,t,-2], u 2 (...

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