Final Exam Solutions

# 1 4 4xy 3y2 a xy 0 2 2 3 0 2 2 3 x y 1 5 42 21 4 5 1

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Unformatted text preview: −2 −2 3 =− 0 −2 −2 3 x y 1 5 42 21 =− + 4 5 1 −2 −2 4 4 1 ( 2x + y ) 2 + ( x − 2y ) 2 5 5 , Final Exam, December [6] Solve the recurrence relation f(0) = a, f(n + 1) f(n) = f(1) = b, 3 −2 1 0 n b a f(n) = 3 f(n − 1) − 2 f(n − 2) = −1 2 −1 2 b a + 2n f(n) = ( − b + 2a) + 2n (b − a) 2 −2 1 −1 b a , Final Exam, December [7] Find eAt where A is the matrix 121 A = 0 2 0 121 λ = 0, 2, 2 eAt 1 0 −1 101 020 2t 1 e 0 + 0 2 0 + te2t 0 0 0 = 00 2 2 −1 0 1 101 020 , Final Exam, December [8] Solve the di erential equation y = Ay where −2 2 −1 A = −1 1 −2 , −1 1 1 2 y(0) = 0 1 λ = 0, 0, 0 3 −3 −3 100 −2 2 −1 2 t 3 −3 −3 = 0 1 0 + t −1 1 −2 + 2 0 0 0 001 −1 1 1 eAt 3 2 −5 t2 3 y = 0 + t −4 + 2 0 1 −1 ,...
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## This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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