2132worksheet4

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

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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]...
View Full Document

## 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.

### Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online